Quadratic Equation Solver
Solve quadratic equations (ax² + bx + c = 0). Shows roots, discriminant, and factored form — all in your browser, instant results.
About the Quadratic Equation Solver
This quadratic equation solver runs entirely in your browser. Enter the coefficients a, b, and c, and the tool solves ax² + bx + c = 0, showing the discriminant, the nature of the roots, both roots (real or complex), the factored form, and the vertex of the parabola.
How it works
The calculator uses the discriminant Δ = b² − 4ac to determine the nature of the roots, then applies the quadratic formula:
x = (−b ± √Δ) / (2a)
- If Δ > 0: two distinct real roots.
- If Δ = 0: one repeated real root.
- If Δ < 0: two complex conjugate roots.
Frequently asked questions
Does this tool upload my data? No. All calculations happen locally in your browser.
What happens when a is 0? The equation is not quadratic. The tool will warn you and solve it as a linear equation.
Are decimals and negative coefficients supported? Yes. Any real values for a, b, and c work.
How is the factored form computed? If the roots are real, the equation is shown as a(x − r₁)(x − r₂) = 0.