MATH TOOL
Quadratic Equation Solver
Solve ax² + bx + c = 0 for real or complex roots, with discriminant and vertex.
Solving ax² + bx + c = 0
Roots
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Discriminant (b² − 4ac)
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Vertex
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Hover the curve to read x and y at any point. Real roots (if any) are marked where the curve crosses the x-axis.
About this tool
Solve any quadratic equation ax² + bx + c = 0 for its roots using the quadratic formula, and see the discriminant and vertex along with it — covers real roots, a repeated root, and complex roots when the discriminant is negative.
Frequently asked questions
- What does the discriminant tell you?
- Its sign determines the type of roots before you even solve: positive means two distinct real roots, zero means exactly one repeated real root, and negative means two complex (non-real) roots.
- What happens with complex roots?
- They're shown in standard a ± bi form — the real part is always −b/2a, and the imaginary part comes from the square root of the negative discriminant.
- What is the vertex used for?
- It's the turning point of the parabola y = ax² + bx + c — the minimum point if a > 0, or the maximum if a < 0 — found at x = −b/2a, useful for graphing or optimization problems.