Quadratic Formula Calculator

Solve ax² + bx + c = 0 — real and complex roots with step-by-step work

x² + x + = 0
x = ?
Roots

About the Quadratic Formula Calculator

This calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. It computes the discriminant to determine the nature of the roots — two real roots when D > 0, one real root when D = 0, and complex conjugate roots when D < 0 — with a full step-by-step breakdown.

The Formula

Discriminant: D = b² − 4ac
Roots: x = (−b ± √D) / (2a)
When D > 0: Two real roots
When D = 0: One real root (repeated)
When D < 0: Two complex roots

FAQs

What does the discriminant tell you?

The discriminant (D = b² − 4ac) determines the nature of roots. If D > 0, there are two distinct real roots. If D = 0, one real root (double root). If D < 0, two complex conjugate roots.

What happens if a = 0?

If a = 0, the equation is no longer quadratic — it becomes linear (bx + c = 0). The calculator requires a non-zero value for a.