Editing Discriminant (section)

===Degree 2===
{{see also|Quadratic equation#Discriminant}}

The quadratic polynomial <math>ax^2+bx+c \,</math> has discriminant
:<math>b^2-4ac\,.</math>

The square root of the discriminant appears in the [[quadratic formula]] for the roots of the quadratic polynomial:
:<math>x_{1,2}=\frac{-b \pm \sqrt {b^2-4ac}}{2a}.</math>

where the discriminant is zero if and only if the two roots are equal. If {{math|''a'', ''b'', ''c''}} are real numbers, the polynomial has two distinct real roots if the discriminant is positive, and two [[complex conjugate]] roots if it is negative.<ref>{{cite book
|title=Integers, polynomials, and rings
|first1=Ronald S.
|last1=Irving
|publisher=Springer-Verlag New York, Inc.
|year=2004
|isbn=0-387-40397-3
|url=https://books.google.com/books?id=B4k6ltaxm5YC&pg=PA154
|at=ch. 10.3 pp. 153–154}}</ref>

The discriminant is the product of {{math|''a''{{sup|2}}}} and the square of the difference of the roots.

If {{math|''a'', ''b'', ''c''}} are [[rational number]]s, then the discriminant is the square of a rational number if and only if the two roots are rational numbers.