second degree polynomials ?

the question asks:
 
write a second degree polynimial equation with real coefficients and the given root.
 
4+2i
 

recall that if z is a root of a real polynomial p, then so is the conjugate z*. you're given 4 + 2i is a root, so the conjugate 4 - 2i is also a root. since your real polynomial must be second degree, these are the only roots. so consider 
 
p(x) = (x - (4 + 2i))(x - (4 - 2i)) = ((x - 4) - 2i)((x - 4) + 2i)
 
and use the formula (a - b)(a + b) = a2 - b2 with a = x - 4 and b = 2i to obtain 
 
p(x) = (x - 4)^2 - (2i)^2 = (x - 4)^2 - (-4) = (x - 4)^2 + 4.
 
now expand (x - 4)^2 = x^2 - 8x + 16 to get 
 
p(x) = x^2 - 8x + 20.
 
the polynomial p satisfies all the desired conditions.