Quadratic Equation Solver

Solve ax² + bx + c = 0 for both roots, with the discriminant and the vertex of the parabola.

Runs in your browser — nothing is uploaded

About the Quadratic Equation Solver

A quadratic equation has the form ax² + bx + c = 0. Its solutions are where the parabola y = ax² + bx + c crosses the x axis. The quadratic formula gives both solutions directly from the coefficients, and the discriminant b² − 4ac tells you what kind of solutions to expect.

A positive discriminant gives two distinct real roots, zero gives one repeated root, and a negative discriminant gives two complex roots. The calculator also reports the vertex, the lowest or highest point of the parabola, which is useful for optimisation problems.

FAQ

Quadratic Equation Solver — frequently asked

What is the quadratic formula?

x = (−b ± √(b² − 4ac)) / (2a). Substitute your coefficients, compute the discriminant under the square root, then calculate the two values with plus and minus.

What if a is zero?

Then the equation is linear, not quadratic. The calculator asks you to enter a non-zero a. For bx + c = 0 the solution is x = −c / b.

What does a complex root mean?

It means the parabola does not cross the x axis. The roots are conjugate pairs of the form p ± qi, where i is the square root of −1. They appear in engineering, signal processing and physics.

How do I find the maximum or minimum?

The vertex is at x = −b / (2a). If a is positive the parabola opens upward and the vertex is a minimum; if a is negative it opens downward and the vertex is a maximum.

Why do I get very small decimals?

Rounding inside floating-point arithmetic can show values such as 0.0000001 where the exact answer is zero, especially for repeated roots. Treat tiny values near zero as zero.

Is my input stored?

No. The coefficients are used only in your browser.