Math

Quadratic Equation Solver

Quadratic formula calculator for real and complex roots, discriminant, axis of symmetry, and vertex.

Solve a quadratic equation in standard form: ax² + bx + c = 0, where a cannot equal zero. The discriminant b² − 4ac determines whether roots are distinct real values, one repeated value, or a complex-conjugate pair.

Decimal results are rounded for display. Keep symbolic values when an exact classroom answer is required.

Frequently asked questions

What if a equals zero?

Then the equation is linear rather than quadratic, so the quadratic formula does not apply.

What does a negative discriminant mean?

The equation has two complex-conjugate roots and no real x-intercepts.

Can the two roots be identical?

Yes. A zero discriminant produces one repeated real root.