Assertion: real number's root | /r/HasProperty | real
Facets:
value: necessarily
type: DEGREE
Source sentences:
text: When one needs to find the roots of an equation, such as for a quadratic equation, one can use the discriminant to see if the roots are real, imaginary, rational or irrational.
text: The solution in radicals (without trigonometric functions) of a general cubic equation contains the square roots of negative numbers when all three roots are real numbers, a situation that cannot be rectified by factoring aided by the rational root test if the cubic is irreducible (the so-called casus irreducibilis).
text: If the square root is to be a real number, then the radicand may not be negative.
text: The roots r of factors of degree one are necessarily real, and replacing x by r gives an embedding of F into R; the number of such embeddings is equal to the number of real roots of f. Restricting the standard absolute value on R to F gives an archimedean absolute value on F; such an absolute value is also referred to as a real place of F.