Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0. Enter coefficients a, b, and c to find the roots, discriminant, and vertex.
The Quadratic Formula
For any equation of the form ax² + bx + c = 0, the roots are:
x = (−b ± √(b² − 4ac)) / 2a
The Discriminant
| Discriminant (Δ = b²−4ac) | Root Type |
|---|---|
| Δ > 0 | Two distinct real roots |
| Δ = 0 | One repeated real root |
| Δ < 0 | Two complex (imaginary) roots |
Example: x² − 5x + 6 = 0
a=1, b=−5, c=6. Discriminant = 25−24 = 1. Roots: x = (5±1)/2, so x=3 and x=2.