Leaving Certificate Mathematics Definitions Practice Test

The discriminant tells you what kind of roots a quadratic will have, and it comes directly from the quadratic formula. For ax^2 + bx + c, the roots are x = [-b ± sqrt(b^2 - 4ac)] / (2a), so the expression under the square root, b^2 - 4ac, determines the nature of the roots. That makes b^2 - 4ac the correct discriminant.

If the discriminant is positive, you get two real and distinct roots; if it’s zero, a repeated real root; if it’s negative, complex roots. The other expressions listed don’t come from the quadratic formula’s radicand, so they don’t correctly characterize the roots.