Quadratic Equation Solver
Enter the coefficients a, b and c to find the roots, discriminant and vertex of a quadratic equation.
How to use it
- Enter coefficient a The number multiplying x². It can't be zero.
- Enter b and c The linear and constant terms.
- Read the roots See real or complex roots and the vertex.
Examples
| x² − 3x + 2 | x = 1, 2 |
|---|---|
| x² + 1 | ±i |
About this tool
The quadratic formula is one of the most-used results in algebra, but it’s easy to slip up on signs and square roots. This solver applies it exactly for any coefficients you enter, including the awkward cases where the roots turn out to be complex.
As well as the roots it reports the discriminant — which tells you what kind of solutions to expect — and the vertex of the parabola, handy for graphing. All of it is computed in your browser.
Frequently asked questions
What does the discriminant tell me?
The discriminant b² − 4ac decides the roots: positive gives two real roots, zero gives one repeated root, and negative gives a complex conjugate pair.
Does it handle complex roots?
Yes. When the discriminant is negative the solver reports the roots as a real part plus or minus an imaginary part.
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Updated June 13, 2026