Discriminant

The discriminant of a Quadratic Equation of the form is the quantity . When are real, this is a notable quantity, because if the discriminant is positive, the equation has two real roots; if the discriminant is negative, the equation has two nonreal roots; and if the discriminant is 0, the equation has a real double root.

Example Problems

Introductory

• (AMC 12 2005) There are two values of a for which the equation has only one solution for x. What is the sum of these values of a?

Solution: Since we want the a's where there is only one solution for x, the discriminant has to be 0. . The sum of these values of a is -16.

Intermediate

• 1977 Canadian MO Problem 1

Other resources

• Wikipedia entry