Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle ay^ {2} +y (2am+b) +\ kushoto (am ^ {2} +bm+c\ kulia) =0\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hatujaweka hali ya pili juu ya y na m, kwa hiyo sasa tunachagua m ili muda wa kati utoke.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hiyo ni, 2<i>am + b = 0 au m = -b/2<i>a.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kutoa mrefu mara kwa mara kutoka pande zote mbili za equation (kuhamisha kwa upande wa kulia) na kisha kugawa kwa anatoa:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

m


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

m


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle y^ {2} = {\ frac {-\ kushoto (am^ {2} +bm+c\ kulia)} {a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kubadilisha kwa m hutoa:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle y^ {2} = {\ frac {-\ kushoto ({\ frac {b ^ {2}} {4a}} + {\ frac {-b ^ {2}} {2a}} +c\ haki)} {a}} = {\ frac {b ^ {2} -4ac} {4a^ {2}}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa hiyo,


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle y=\ pm {\ frac {\ sqrt {b ^ {2} -4ac}} {2a}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

kubadilisha x = y + m = y -b/2<i>a hutoa formula ya quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x= {\ frac {-b\ pm {\ sqrt {b ^ {2} -4ac}} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa kutumia utambulisho wa algebraic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia ifuatayo ilitumiwa na wanahisabati wengi wa kihistoria: [11]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hebu mizizi ya equation ya quadratic ya kawaida iwe r1 na r2.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Derivation huanza kwa kukumbuka utambulisho:


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle (r_ {1} -r_ {2}) ^ {2} = (r_ {1} +r_ {2}) ^ {2} -4r_ {1} r_ {2}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kuchukua mizizi ya mraba pande zote mbili, tunapata:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {1} -r_ {2} =\ pm {\ sqrt {(r_ {1} +r_ {2}) ^ {2} -4r_ {1} r_ {2}}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Tangu mgawo a 合 0, tunaweza kugawanya equation kiwango na kupata quadratic polynomial kuwa mizizi sawa.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Yaani,


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x^ {2} + {\ frac {b} {a}} x+ {\ frac {c} {a}} = (x-r_ {1}) (x-r_ {2}) =x^ {2} - (r_ {1} +r_ {2}) x+r_ {1} r_ {2}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kutoka hili tunaweza kuona kwamba jumla ya mizizi ya equation ya quadratic ya kawaida hutolewa na -b/a, na bidhaa za mizizi hiyo hutolewa na c/a.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hivyo utambulisho unaweza kuandikwa upya kama:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {1} -r_ {2} =\ pm {\ sqrt {\ kushoto (- {\ frac {b} {a}}\ haki) ^ {2} -4 {\ frac {c} {a}}}} =\ pm {\ sqrt {\ frac {\ frac {b {2}} {a^ {2}}} - {\ frac {\ frac {\ frac 4ac} {a^ {2}}}}} =\ pm {\ frac {\ sqrt {b ^ {2} -4ac}} {a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Sasa,


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {1} = {\ frac {(r_ {1} +r_ {2}) + (r_ {1} -r_ {2})} {2}} = {\ frac {\ frac {b} {a}}\ pm {\ frac {\ sqrt {b^ {2} -4ac}}} {a}} 2 {a}}}} = {\ frac {-b\ pm {\ sqrt {b ^ {2} -4ac}} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Tangu r2 = -r1 - b/a, ikiwa tunachukua


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {1} = {\ frac {-b+ {\ sqrt {b ^ {2} -4ac}}} {2a}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

basi sisi kupata


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {2} = {\ frac {-b- {\ sqrt {b ^ {2} -4ac}} {2a}}\\;}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

na kama sisi badala yake kuchukua


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {1} = {\ frac {-b- {\ sqrt {b ^ {2} -4ac}}} {2a}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

basi sisi mahesabu kwamba


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {2} = {\ frac {-b+ {\ sqrt {b ^ {2} -4ac}} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kuchanganya matokeo haya kwa kutumia shorthand ya kawaida ±, tuna kwamba ufumbuzi wa equation quadratic hutolewa na:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x= {\ frac {-b\ pm {\ sqrt {b ^ {2} -4ac}} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

By Lagrange resolvents


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia mbadala ya kupata formula quadratic ni kupitia njia ya Lagrange resolvents, [12] ambayo ni sehemu ya awali ya nadharia ya Galois. [13]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia hii inaweza kuwa ya jumla ya kutoa mizizi ya polynomials za ujazo na polynomials quartic, na inaongoza kwa nadharia ya Galois, ambayo inaruhusu mtu kuelewa ufumbuzi wa equations algebraic ya shahada yoyote katika suala la kundi ulinganifu wa mizizi yao, kundi la Galois.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia hii inalenga mizizi zaidi kuliko upya upya equation ya awali.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kutokana na monic quadratic polynomial


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x^ {2} +px+q\\,}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

kudhani kuwa ni sababu kama


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ kuonyesha style x^ {2} +px+q= (x-\ alpha) (x-\ beta)\\,}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kupanua mavuno


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x^ {2} +px+q=x^ {2} - (\ alpha +\ beta) x+\ alpha\ beta\\,}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

ambapo p = - (α + β) na q = αβ.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa kuwa utaratibu wa kuzidisha haijalishi, mtu anaweza kubadili α na β na maadili ya p na q hayatabadilika: mtu anaweza kusema kwamba p na q ni polynomials ya ulinganifu katika α na β.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa kweli, ni polynomials ya msingi ya ulinganifu — polynomial yoyote ya ulinganifu katika α na β inaweza kuelezwa kwa suala la α + β na αβ Njia ya nadharia ya Galois ya kuchambua na kutatua polynomials ni: kutokana na coefficients ya polynomial, ambayo ni kazi ya ulinganifu katika mizizi, mtu anaweza “kuvunja ulinganifu “Na kurejesha mizizi?


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hivyo kutatua polynomial ya shahada n ni kuhusiana na njia za upya (“kuruhusu”) kwa maneno, ambayo inaitwa kundi linganifu juu ya n barua, na inaashiria Sn.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa polynomial quadratic, njia pekee ya kupanga upya maneno mawili ni kubadili yao (“transpose” yao), na hivyo kutatua polynomial quadratic ni rahisi.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ili kupata mizizi α na β, fikiria jumla na tofauti zao:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} r_ {1} &=\ alpha +\ beta\\ r_ {2} &=\ alpha -\ beta\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hizi huitwa resolvents ya Lagrange ya polynomial; tazama kwamba moja ya haya inategemea utaratibu wa mizizi, ambayo ni hatua muhimu.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Mtu anaweza kurejesha mizizi kutoka kwa resolvents kwa inverting equations hapo juu:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa}\ alpha &=\ textstyle {\ frac {1} {2}}\ kushoto (r_ {1} +r_ {2}\ haki)\\ beta &=\ textstyle {\ frac {1} {2}}\ kushoto (r_ {1} -r_ {2}\ haki)\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hivyo, kutatua kwa ufumbuzi hutoa mizizi ya awali.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Sasa r1 = α + β ni kazi ya ulinganifu katika α na β, hivyo inaweza kuelezwa kwa suala la p na q, na kwa kweli r1 = -p kama ilivyoelezwa hapo juu.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Lakini r2 = α - β si ulinganifu, kwani kubadili α na β huzaa -r2 = β - α (rasmi, hii inaitwa hatua ya kikundi cha kundi linganifu la mizizi).


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa kuwa r2 haipatikani, haiwezi kuonyeshwa kwa suala la coefficients p na q, kwa kuwa hizi zina ulinganifu katika mizizi na hivyo ni maneno yoyote ya polynomial yanayowashirikisha.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kubadilisha utaratibu wa mizizi hubadilisha tu r2 kwa sababu ya -1, na hivyo mraba r22 = (α - β) 2 ni sawa katika mizizi, na hivyo inaelezewa kwa p na q.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kutumia equation


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle (\ alpha -\ beta) ^ {2} = (\ alpha +\ beta) ^ {2} -4\ alpha\ beta\\}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

mavuno


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {2} ^ {2} =p^ {2} -4q\\}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

na hivyo


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle r_ {2} =\ pm {\ sqrt {p^ {2} -4q}}\\}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ikiwa mtu anachukua mizizi nzuri, kuvunja ulinganifu, mtu hupata:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic

r


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} r_ {1} &=-p\\ r_ {2} &= {\ sqrt {p^ {2} -4q}}\ mwisho {iliyokaa}}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

na hivyo


Question: Nini formula ya quadratics?

Fomu ya Quadratic

α


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

β


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa}\ alpha &= {\ tfrac {1} {2}}\ kushoto (-p+ {\ sqrt {p^ {2} -4q}}\ haki)\\ beta &= {\ tfrac {1} {2} {2} {2}\ haki)\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hivyo mizizi ni


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle\ textstyle {\ frac {1} {2}}\ kushoto (-p\ pm {\ sqrt {p^ {2} -4q}}\ kulia)}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

ambayo ni formula ya quadratic.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kutoa p = b/a, q = c/a hutoa fomu ya kawaida kwa wakati quadratic sio monic.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Resolvents inaweza kutambuliwa kama r1/2 = -p/2 = -b/2<i>kuwa kipeo, na r22 = p2 - 4<i>q ni ubaguzi (wa polynomial monic).


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia sawa lakini ngumu zaidi inafanya kazi kwa equations za ujazo, ambapo moja ina resolvents tatu na equation quadratic (“kutatua polynomial”) zinazohusiana na r2 na r3, ambayo mtu anaweza kutatua kwa equation quadratic, na pia kwa equation quartic (shahada 4), ambao kutatua polynomial ni cubic, ambayo inaweza kwa upande kutatuliwa. [12]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia sawa ya equation quintic hutoa polynomial ya shahada 24, ambayo haina kurahisisha tatizo, na, kwa kweli, ufumbuzi wa equations quintic kwa ujumla hauwezi kuelezwa kwa kutumia mizizi tu.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

By extrema


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kujua thamani ya x katika hatua ya kazi kali hufanya iwezekanavyo kutatua tu kwa ongezeko (au kupungua) inahitajika katika x kutatua equation quadratic.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia hii inatumia kwanza upambanuzi ili kupata thamani x kwa mwisho, inayoitwa ext.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Sisi kisha kutatua kwa thamani, q, kwamba kuhakikisha kwamba f (ext + q) = 0.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ingawa hii inaweza kuwa njia angavu zaidi, inahakikisha kwamba hisabati ni moja kwa moja.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

f


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

f


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} f


Question: Nini formula ya quadratics?

Fomu ya Quadratic

(x) &=ax^ {2} +bx+c\\ [5pt] {\ frac {\ sehemu f} {\ sehemu x}} &=2ax+b\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kuweka tofauti ya juu kwa sifuri itatupa extrema ya kazi ya quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic

ext


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x_ {\ maandishi {ext}} = {\ frac {-b} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Tunafafanua q kama ifuatavyo:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic

ext


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle q=x_ {0} -x_ {\ maandishi {ext}}\\,}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hapa x0 ni thamani ya x ambayo hutatua equation quadratic.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Jumla ya maandishi na kutofautiana kwa riba, q, imeingia kwenye equation ya quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Δ


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

q


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} a\ kushoto ({\ frac {-b} {2a}} +q\ haki) ^ {2} +b\ kushoto ({\ frac {-b} {2a}} +q\ haki) +c & = 0\\ [5pt]\ kushoto ({\ frac {-b} {2a}} +q\ haki) ^ {2} + {2} {\ frac {b} {a}}\ kushoto ({\ frac {-b} {2a}} +q\ haki) + {\ frac {c} {a}} &=0&& (a\ neq 0)\\ [5pt] {\ frac {b^ {2}} {4a^ {2}} +q^ {2} - {\ frac {bq {bq} {a} - {\ frac {b^ {2}} {2a^ {2}}} + {\ frac {bq} {a}} + {\ frac {c} {a}} &=0\\ [5pt] {\ frac {-b^ {2}} {4a^ {2}}} +q^ {2} + {\ frac {c} {a} {a}} &=0\\ [5pt] q^ {2} &= {\ frac {2} -4ac} {4ac} {4a^ {2}}}\\ [5pt] q&= {\ frac {\ pm {\ sqrt {\ sqrt {b ^ {2} -4ac}} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Thamani ya x katika hatua kali ni kisha aliongeza kwa pande zote mbili za equation


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x_ {0} = {\ frac {-b\ pm {\ sqrt {b ^ {2} -4ac}} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hii inatoa formula ya quadratic.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa njia hii mtu anaepuka mbinu ya kukamilisha mraba na hesabu ngumu zaidi haihitajiki.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kumbuka ufumbuzi huu ni sawa na kutatua kupata formula kwa kubadilisha.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa kugawanyika katika sehemu halisi na za kufikiri


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Fikiria equation


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

z


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

z


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle az^ {2} +bz+c=0}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

wapi


Question: Nini formula ya quadratics?

Fomu ya Quadratic

z


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle z=x+iy}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

ni idadi tata na ambapo a, b, na c ni namba halisi.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kisha


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} a (x+iy) ^ {2} +b (x+iy) +c&=0\\,\ a (x^ {2} -y {2} +i2xy) +b (x+iy) +c=0\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hii inagawanyika katika equations mbili, sehemu halisi:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ kuonyesha style a (x^ {2} -y ^ {2}) +bx+c=0}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

na sehemu ya kufikiri:


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ kuonyesha style 2axy+na = 0\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kudhani kwamba


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Δ


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle y\ mpya 0}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

kisha ugawanye equation ya pili na y:


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ kuonyesha style 2ax+b = 0}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

na kutatua kwa x:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ kuonyesha style x = {-b\ zaidi ya 2a}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Badilisha thamani hii kwa x katika equation ya kwanza na kutatua kwa y:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} a {\ Big (} {b ^ {2}\ juu ya 4a^ {2}} -y {2} {\ Big)} - {b ^ {2}\ juu ya 2a} +c&= 0\\ {b ^ {2}\\ b {2} - {2b ^ {2}\ zaidi ya 4a} +c&=0\\ {-b^ {2}\ juu ya 4a} -ay^ {2} +c&= 0\\ ay^ {2} + {b ^ {2}\ juu ya 4a} -c&=0\\ y ^ {2} &= {c\ juu ya} - {b ^ {2}\ zaidi ya 4a^ {2}}\\ y&=\ pm {\ sqrt {c\ juu ya a} - {b ^ {2}\ zaidi ya 4a^ {2}}}} = {\ pm {\ sqrt {\ sqrt {ca- {b^ {2}\ zaidi ya 4}}}\ juu ya} = {\ pm {\ sqrt {4ca-b^ {2}}}\ zaidi ya 2a}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Tangu


Question: Nini formula ya quadratics?

Fomu ya Quadratic

z


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle z=x+iy}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

, basi


Question: Nini formula ya quadratics?

Fomu ya Quadratic

z


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

i


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

z


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle {\ kuanza {iliyokaa} z&= {-b\ juu ya 2a}\ pm {\ sqrt {\ sqrt {4ac-b ^ {2}}}\ zaidi ya 2a}\\ [5pt] z&= {-b\ juu ya 2a}\ pm {\ sqrt {\ sqrt {b ^ {2} -4ac}\ zaidi ya 2a} = {-b\ pm {\ sqrt {\ sqrt {\ sqrt ^ {2} -4ac}}\ zaidi ya 2a}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

\ mwisho {iliyokaa}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ingawa y ilikuwa kudhani kuwa yasiyo ya sifuri, formula hii ya mwisho inafanya kazi kwa mizizi yoyote ya equation ya awali, wakati kuchukua kwamba


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle y=0}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

zinageuka kuwa na msaada mkubwa (usio na maana na mviringo).


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Maendeleo ya kihistoria


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Njia za mwanzo za kutatua equations quadratic zilikuwa kijiometri.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Vidonge vya cuneiform vya Babeli vina matatizo yanayoweza kupunguzwa ili kutatua milinganyo ya quadratic. [15]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Misri Berlin Papyrus, dating nyuma ya Ufalme wa Kati (2050 BC hadi 1650 BC), ina ufumbuzi wa equation quadratic mbili mrefu.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Mtaalamu wa hisabati wa Kigiriki Euclid (karibu 300 KK) alitumia mbinu za kijiometri kutatua milinganyo ya quadratic katika Kitabu cha 2 cha Elements zake, makala yenye ushawishi mkubwa wa hisabati. [17]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kanuni za equations quadratic zinaonekana katika Kichina Sura tisa juu ya Sanaa ya Hisabati circa 200 KK. [18] [19]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Katika kazi yake Arithmetica, mtaalamu wa hisabati wa Kigiriki Diophantus (karibu 250 KK) alitatua milinganyo ya quadratic kwa njia inayojulikana zaidi algebraic kuliko algebra ya kijiometri ya Euclid. [17]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Suluhisho lake linatoa mzizi mmoja tu, hata wakati mizizi yote ni chanya. [20]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Mtaalamu wa hisabati wa India Brahmagupta (597—668 AD) alielezea wazi formula ya quadratic katika makala yake Brāhmasphuhasiddhānta iliyochapishwa mwaka 628 BK, [21] lakini imeandikwa kwa maneno badala ya alama. [22]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Suluhisho lake la equation quadratic ax2 + bx = c ilikuwa kama ifuatavyo: “Kwa idadi kamili imeongezeka kwa mara nne [mgawo wa] mraba, ongeza mraba wa [mgawo wa] muda wa kati; mizizi ya mraba ya sawa, chini ya [mgawo wa] muda wa kati, kugawanywa na mara mbili [ mgawo wa mraba] ni thamani. “[23]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hii ni sawa na:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x= {\ frac {\ sqrt {4ac+b ^ {2}}} -b} {2a}}\\.


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Mtaalamu wa hisabati wa karne ya 9 Muhammad ibn Mūsā al-Khwārizmī alitatua milinganyo ya quadratic algebraically. [24]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Fomu ya quadratic inayofunika kesi zote ilipatikana kwanza na Simon Stevin mwaka 1594. [25] Mwaka 1637 René Descartes alichapisha La Géométrie iliyo na matukio maalum ya formula ya quadratic katika fomu tunayojua leo.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Muonekano wa kwanza wa suluhisho la jumla katika fasihi za kisasa za hisabati ulionekana katika karatasi ya 1896 na Henry Heaton. [26]


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Matumizi muhimu


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Umuhimu wa kijiometri


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kwa upande wa kuratibu jiometri, parabola ni Curve ambao (x,


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y) -kuratibu ni ilivyoelezwa na polynomial ya shahada ya pili, i.e. equation yoyote ya fomu:


Question: Nini formula ya quadratics?

Fomu ya Quadratic

y


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

p


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ kuonyesha style y=p


Question: Nini formula ya quadratics?

Fomu ya Quadratic

(x) =a_ {2} x^ {2} +a_ {1} x+a_ {0}\\,}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

ambapo p inawakilisha polynomial ya shahada ya 2 na a0, a1, na a2 合 0 ni coefficients ya mara kwa mara ambazo scripts zinahusiana na shahada ya muda wao.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Tafsiri ya kijiometri ya formula ya quadratic ni kwamba inafafanua pointi kwenye mhimili wa x-ambapo parabola itavuka mhimili.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Zaidi ya hayo, ikiwa formula ya quadratic ilionekana kama maneno mawili,


Question: Nini formula ya quadratics?

Fomu ya Quadratic

x


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

b


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

c


Question: Nini formula ya quadratics?

Fomu ya Quadratic


Question: Nini formula ya quadratics?

Fomu ya Quadratic

a


Question: Nini formula ya quadratics?

Fomu ya Quadratic

{\ displaystyle x= {\ frac {-b\ pm {\ sqrt {b ^ {2} -4ac\}} {2a}} =- {\ frac {b} {2a}}\ pm {\ frac {\ frac {\ sqrt {b ^ {2} -4ac\}} {2a}}}


Question: Nini formula ya quadratics?

Fomu ya Quadratic

mhimili wa ulinganifu unaonekana kama mstari x = -b/2<i>a.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Neno lingine, √B2 - 4<i>ac/2<i>a, hutoa umbali wa zero ziko mbali na mhimili wa ulinganifu, ambapo ishara ya pamoja inawakilisha umbali wa kulia, na ishara ndogo inawakilisha umbali wa kushoto.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ikiwa neno hili la umbali lilipungua hadi sifuri, thamani ya mhimili wa ulinganifu itakuwa thamani ya x ya sifuri pekee, yaani, kuna suluhisho moja tu linalowezekana kwa equation ya quadratic.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Algebraically, hii ina maana kwamba √B2 - 4<i>ac = 0, au tu b2 - 4<i>ac = 0 (ambapo upande wa kushoto ni inajulikana kama ubaguzi).


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hii ni moja ya matukio matatu, ambapo wabaguzi anaonyesha ngapi zero za parabola zitakuwa nazo.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ikiwa mtu anayebagua ni chanya, umbali utakuwa usio na sifuri, na kutakuwa na ufumbuzi wawili.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hata hivyo, pia kuna kesi ambapo ubaguzi ni chini ya sifuri, na hii inaonyesha umbali itakuwa imaginary - au baadhi nyingi ya kitengo tata i, ambapo i = √-1 - na zeros parabola ya itakuwa namba tata.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Mizizi ngumu itakuwa conjugates ngumu, ambapo sehemu halisi ya mizizi tata itakuwa thamani ya mhimili wa ulinganifu.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hakutakuwa na maadili halisi ya x ambapo parabola huvuka mhimili wa x.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Uchunguzi wa vipimo


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Ikiwa mara kwa mara a, b, na/au c sio unitless, basi vitengo vya x lazima iwe sawa na vitengo vya b/a, kutokana na mahitaji ambayo ax2 na bx wanakubaliana juu ya vitengo vyao.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Zaidi ya hayo, kwa mantiki hiyo, vitengo vya c lazima iwe sawa na vitengo vya b2/a, ambavyo vinaweza kuthibitishwa bila kutatua kwa x.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Hii inaweza kuwa chombo chenye nguvu cha kuthibitisha kuwa usemi wa quadratic wa kiasi cha kimwili umeanzishwa kwa usahihi, kabla ya kutatua.


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Angalia pia


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Kubagua


Question: Nini formula ya quadratics?

Fomu ya Quadratic

Theorem ya msingi ya algebra


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Ukurasa Kuu


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna (retitled Madonna: The First Album for 1985 re-release) ni albamu ya kwanza na mwimbaji wa Kimarekani Madonna, iliyotolewa tarehe 27 Julai 1983 na Sire Records.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Baada ya kuanzisha mwenyewe kama mwimbaji katika jiji la New York City, Madonna ulisainiwa na Rais Sire Seymour Stein, kutokana na mafanikio ya single yake ya kwanza, “Kila mtu” (1982).


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Alikuwa mwandishi pekee kwa nyimbo nyingi za albamu, na akamchagua Reggie Lucas kama mtayarishaji wake wa msingi.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Haifurahi na matokeo ya uzalishaji wa Lucas, alimalika John “Jellybean” Benitez kukamilisha albamu, ambaye alichanganya nyimbo tatu na kutunga “Holiday”.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna ina upbeat synthetic disco sauti, kwa kutumia teknolojia mpya ya wakati, ikiwa ni pamoja na Linn ngoma mashine, Moog bass na Oberheim OB-X synthesizer.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Aliimba katika timbre mkali, girlish, na lyrics kuhusu upendo na mahusiano.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Ili kukuza albamu hiyo, Madonna alifanya gigs moja-off katika klabu na kwenye televisheni nchini Marekani na Uingereza katika 1983 na 1984, ikifuatiwa na The Virgin Tour mwaka 1985.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Single tano zilitolewa, ikiwa ni pamoja na hits ya kimataifa ya juu kumi “Holiday”, “Lucky Star”, na “Borderline”.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Video zao za muziki zinazoambatana zilitolewa kwenye mkusanyiko wa video ya Madonna, ambayo ikawa video bora kuuza ya 1985 nchini Marekani.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna kushika nafasi ya namba nane kwenye Billboard 200, na alithibitishwa mara tano platinum na Recording Industry Association of America (RIAA) kwa ajili ya usafirishaji wa nakala milioni tano nchini Marekani.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Ilifikia kumi ya juu ya chati hizo nchini Australia, Ufaransa, Uholanzi, New Zealand, Sweden na Uingereza, na kuuza zaidi ya nakala milioni 10 duniani kote.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Albamu ilipokea mapitio mazuri kwa ujumla kutoka kwa wakosoaji wa muziki na ilikuwa nafasi ya tano kwenye orodha ya Entertainment Weekly ya “Top 100 Albamu Bora za Past 25 Years” mnamo 2008.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Albamu imekuwa sifa kwa kuweka kiwango cha dance-pop kwa miongo kadhaa baadaye, na kwa kuelekeza mwelekeo kwa wasanii wengi wa kike wa miaka ya 1980.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Background


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Mwaka 1982, Madonna, mwenye umri wa miaka 24, alikuwa akiishi mnamo New York, na akijaribu kuanzisha kazi yake ya muziki. [1]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Alijiunga na mpenzi wake wa Detroit Steve Bray ambaye akawa ngoma wa bendi yake, klabu ya Breakfast, ambayo ilicheza kwa ujumla muziki wa hard-rock.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Hivi karibuni waliachana na kucheza nyimbo katika Ghana ya hard-rock, na wakasainiwa na kampuni ya usimamizi wa muziki iitwayo Gotham Records, wakipanga kuhamia katika mwelekeo mpya wa muziki. [2]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Waliamua kujiingiza funk Ghana, lakini kampuni ya rekodi haikuwa na furaha na vipaji vyao vya muziki na walikuwa imeshuka kutoka studio; Madonna na Bray waliacha bendi pia. [1]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wakati huo huo, alikuwa ameandika na kukuza baadhi ya nyimbo peke yake.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Alibeba kanda mbaya za nyimbo tatu, “Everybody”, “Ain't No Big Deal” na “Burning Up”.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wakati huo alikuwa akirudia klabu ya usiku ya Danceteria huko New York.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Ilikuwa hapa kwamba Madonna alimshawishi DJ Mark Kamins kucheza “Kila mtu”. [1]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wimbo ulipokelewa vyema na umati wa watu, na Kamins aliamua kwamba anapaswa kupata Madonna mpango wa rekodi, kwa kuelewa kwamba atapata kuzalisha single. [1]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Alimpeleka kwa bosi wake Chris Blackwell, ambaye alikuwa na Island Records, lakini Blackwell alikataa kutia saini Madonna hivyo wakakaribia Sire Records. [3]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Michael Rosenblatt, ambaye alifanya kazi katika wasanii na repertoire idara ya Sire, alitoa Madonna $5,000 mapema, pamoja na $1,000 katika mirahaba, kwa kila wimbo aliandika. [4] [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna hatimaye alisainiwa kwa mbili 12" single na Rais wa Sire, Seymour Stein, ambaye alikuwa na hisia na kuimba kwake, [4] baada ya kusikiliza “Kila mtu” katika hospitali katika Lenox Hill ambapo alikiri. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Toleo la “12" la “Everybody” lilitayarishwa na Mark Kamins katika Blank Tapes Studios huko New York, ambaye alichukua kazi ya uzalishaji kutoka Steve Bray. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Kurekodi mpya mbio 5:56 upande mmoja na 9:23 kwa toleo dub upande wa nyuma.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna na Kamins alikuwa na rekodi moja kwa gharama zao wenyewe. [6]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Arthur Baker, rafiki wa Mark Kamins, alimuongoza kupitia nafasi ya mtayarishaji wa muziki na kumpatia mwanamuziki wa studio Fred Zarr aliyecheza keyboards kwenye wimbo. [7]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Zarr akawa moja kati ya nyuzi za kawaida za muziki kwenye albamu kwa hatimaye kufanya kwenye kila wimbo.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Kutokana na bajeti iliyozuiliwa kurekodi ilifanyika haraka.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna na Kamins walikuwa na ugumu wa kuelewa pembejeo za kila mmoja kwa vikao.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Rosenblatt alitaka kuachia “Everybody” na “Ain't No Big Deal” upande wa pili, lakini baadaye alibadili mawazo yake na kuweka “Everybody” pande zote mbili za rekodi ya vinyl baada ya kusikia toleo la kumbukumbu la “Ain't No Big Deal”. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Single ilitolewa kibiashara mnamo Oktoba 1982 na ikawa hit ya ngoma nchini Marekani.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Hii ilisababisha Sire kusaini Madonna kwa LP na single mbili zaidi. [4] [8]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Maendeleo


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

“[S] hakuwa na furaha na [albamu] nzima, kwa hiyo niliingia na kumtia tamu muziki mwingi kwa ajili yake, na kuongeza baadhi ya magitaa kwa 'Lucky Star', baadhi ya sauti, baadhi ya uchawi... Mimi nilitaka kufanya kazi bora mimi naweza kufanya kwa ajili yake. Wakati tungependa kucheza 'Holiday' au 'Lucky Star', unaweza kuona kwamba alikuwa amezidiwa na jinsi yote yalivyoonekana.”


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

—Benitez kuzungumza juu ya Madonna na albamu.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

[9] [10]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Albamu ilirekodiwa kimsingi katika Sigma Sound Studios mnamo New York City. [11]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna alichagua kufanya kazi na ama Kamins au Bray, lakini alichagua Reggie Lucas, mtayarishaji Warner Bros.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Bray aliamua kumshinikiza katika mwelekeo wa muziki wa pop, na kurekodi wimbo wa “Burning Up” pamoja naye.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Hata hivyo, Madonna bado hakuwa na nyenzo za kutosha kuzalisha albamu kamili.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Nyimbo zilizopo zilikuwa, “Lucky Star”, toleo jipya la “Ain't No Big Deal”, “Think of Me” na “I Know It”.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Lucas alileta nyimbo nyingine mbili kwenye mradi huo, “Physical Attraction” na “Borderline”. [9]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Kama yeye kumbukumbu ya nyimbo yeye deviated mno kutoka matoleo ya awali ya demos.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wimbo mmoja uliobadilishwa kama huo ulikuwa “Lucky Star”.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wimbo uliandikwa na Madonna kwa ajili ya Kamins, ambaye hapo awali aliahidi kucheza wimbo katika Danceteria. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Hata hivyo, wimbo ulitumiwa badala yake na Madonna kwa albamu, ambayo alipanga kuiita Lucky Star.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Aliamini kuwa “Lucky Star”, pamoja na “Borderline”, walikuwa msingi kamili kwa ajili ya albamu yake. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Matatizo yaliondoka kati yake na Lucas wakati wa kurekodi nyimbo hizo.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna hakuwa na furaha na jinsi matoleo ya mwisho yaligeuka.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Kulingana na Madonna, Lucas alitumia vyombo vingi mno na hakufikiria mawazo yake kwa ajili ya nyimbo. [12]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Hii ilisababisha mzozo kati ya hizo mbili na, baada ya kumaliza albamu, Lucas aliacha mradi bila kushona nyimbo kwa specifikationer ya Madonna; hivyo alimwita John “Jellybean” Benitez, DJ katika Funhouse disco, remix nyimbo zilizopo.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wakati huo huo, kutokana na mgongano wa maslahi, Bray alikuwa ameuza “Ain't No Big Deal” kwa kitendo kwenye studio nyingine, na kuifanya haipatikani kwa mradi wa Madonna. [9]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Ni Benitez ambaye aligundua wimbo mpya, ulioandikwa na Curtis Hudson na Lisa Stevens wa kundi la pop Pure Energy. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Wimbo, ulioitwa “Holiday”, ulikuwa umegeuka chini na Phyllis Hyman na Mary Wilson, zamani wa The Supremes. [13]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Benitez na Madonna alimtuma demo kwa rafiki yao, Fred Zarr ili aweze kupamba utaratibu na mpango mistari synthesizer. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Baada ya sauti zilirekodiwa na Madonna, Benitez alitumia siku nne akijaribu kuimarisha rufaa ya kibiashara ya wimbo kabla ya tarehe ya mwisho ya Aprili 1983. [9] [13]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Kabla ya kukamilika, Madonna na Benitez walikutana na Fred Zarr kwenye Sigma Sound huko Manhattan, ambapo Zarr aliongeza solo ya piano inayojulikana sasa kuelekea mwisho wa wimbo. [5]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Muziki na lyrics


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Kulingana na AllMusic, Madonnna ni albamu ya dance-pop na post-disco. [14] [15]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

sauti ya jumla ya albamu ni dissonant, na ni katika mfumo wa upbeat synthetic disco, kutumia baadhi ya teknolojia mpya ya wakati, kama matumizi ya Linn ngoma mashine, Moog bass na.


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Vifaa hivi vina tarehe tangu, hivyo sauti ya albamu huja mbali kama kiasi fulani kali. [16]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Madonna alitoa maoni juu ya albamu yake ya kwanza: “Nyimbo zilikuwa dhaifu sana na nilikwenda Uingereza wakati wa rekodi hivyo sikuwa karibu... Sikuwa katika udhibiti. [...] Sikuweza kutambua jinsi ilivyokuwa muhimu kwangu kuvunja nje ya mold disco kabla ningependa kumaliza albamu [kwanza]. Napenda ningekuwa na aina kidogo zaidi huko. “[16] Albamu inaanza na wimbo wa “Lucky Star”, wimbo wa ngoma wa kati-paced, kuanzia na sparkle ya note ya synth na hufuatiwa na mapigo mazito ya ngoma ya elektroniki na handclaps. [16]


Question: Albamu ya kwanza ya Madonna ilikuwa nini?

Madonna (Madonna albamu)

Gitaa inachezwa katika riff high na bubbling bass synth ni zinazozalishwa kuongozana sauti gitaa. [16]