Quadratic Equation Solver
Solve ax² + bx + c = 0, including complex roots, vertex and discriminant.
What the Quadratic Equation Solver does
The quadratic formula solves any equation of the form ax² + bx + c = 0. The discriminant b² − 4ac decides the outcome: positive gives two real roots, zero gives one repeated root, and negative gives a conjugate pair of complex roots.
Formula
x = (−b ± √(b² − 4ac)) ÷ 2aDiscriminant Δ = b² − 4acVertex at x = −b ÷ 2a
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| a (x² coefficient) | number | Yes | — |
| b (x coefficient) | number | Yes | — |
| c (constant) | number | Yes | — |
How to use it
- Enter a (x² coefficient), b (x coefficient) and c (constant).
- Select Calculate.
Worked example
Solve x² − 5x + 6 = 0.
- a
- 1
- b
- -5
- c
- 6
Δ = 25 − 24 = 1, so x = (5 ± 1) ÷ 2, giving roots 3 and 2.
Frequently asked questions
What does the discriminant tell me?
How many times the parabola crosses the x-axis: twice if positive, once (a tangent touch) if zero, never if negative.
What are complex roots useful for?
They show the parabola never meets the x-axis, and they matter in signal processing, control systems and electrical engineering.