ScientificCalcul

Quadratic Equation Calculator

Solve ax²+bx+c=0 with the discriminant and quadratic formula, including repeated, irrational and complex roots, vertex and axis details.

Solve quadratic equations from coefficients a, b and c

Enter the coefficients from ax² + bx + c = 0 to calculate the discriminant and both roots.

The result also reports whether the roots are real or complex, plus the parabola's axis of symmetry and vertex.

Learn the concept

Try these examples

  • 1,-5,6
  • 1,2,1
  • 1,1,1

Quick reference

  • Discriminant: D = b² − 4ac.
  • Roots: x = (−b ± √D)/(2a).
  • Axis of symmetry: x = −b/(2a).

FAQ

What does the discriminant tell me?

A positive discriminant gives two real roots, zero gives one repeated root and a negative value gives two complex roots.

Does this calculator handle complex roots?

Yes. Negative discriminants are returned as a complex conjugate pair.

Sources and review

Last reviewed:

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