Solve ax² + bx + c = 0 for real or complex roots and the discriminant.
| Discriminant | – |
| x₁ | – |
| x₂ | – |
Use this calculator for a true quadratic (a ≠ 0). The discriminant D = b² − 4ac tells the type of roots: D > 0 two distinct reals, D = 0 a repeated real, D < 0 a complex conjugate pair written as p ± qi.
The roots are x = (−b ± √D) / (2a) when D ≥ 0, using the real square root. When D < 0 the same formula is used with √|D| on the imaginary part. a cannot be 0 (that would be linear, not quadratic).
a: Coefficient of x². Cannot be 0.
b: Coefficient of x.
c: Constant term.
Discriminant: b² − 4ac.
x₁: Larger real root, or the +i complex root.
x₂: Smaller real root, or the −i complex root.
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