Solve any quadratic — roots, discriminant, and vertex
Enter a, b and c for ax² + bx + c = 0 and get the roots, the discriminant and the vertex, with the quadratic formula shown.
Result
D = b² − 4ac = (-5)² − 4·1·6 = 1; x = (−b ± √D) ÷ 2a = (5 ± √1) ÷ 2
How is this calculated?
Using the tool
Enter a, b, and c for ax² + bx + c = 0. You get the roots (real, repeated, or complex), the discriminant that tells you which, and the parabola's vertex — with the quadratic formula shown.
The math
The quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a solves any quadratic. The part under the root, the discriminant b² − 4ac, tells you the kind of roots before you finish: positive gives two real roots, zero gives one repeated root, and negative gives two complex roots. The vertex sits at x = −b ÷ 2a — the turning point of the parabola.
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