Discriminant Calculator
The Discriminant Calculator finds b² − 4ac for a quadratic ax² + bx + c and tells you the nature of its roots. Enter the coefficients a, b, and c.
Formula
Discriminant = b² − 4ac
- Positive: two distinct real roots. Zero: one repeated root. Negative: complex roots.
- A perfect-square positive discriminant means the roots are rational.
x² − 5x + 6
Inputs
- a: 1
- b: -5
- c: 6
(−5)² − 4·1·6 = 25 − 24 = 1 > 0, so two distinct real roots (2 and 3).
Frequently asked questions
What does the discriminant tell you?
Whether a quadratic has two real roots, one repeated root, or two complex roots — without solving it.