Quadratic Formula Calculator

How this calculator works

Enter coefficients for ax² + bx + c = 0. A positive discriminant gives two distinct real roots, zero gives a repeated real root and a negative discriminant indicates a complex-conjugate pair. This project’s existing formatter handles real values, so complex cases are classified rather than presented as partial or misleading real answers. The solver scales coefficients and calculates one root without subtracting nearly equal large terms, recovering the other from their product.

Formula

Discriminant D = b²−4ac. Quadratic formula x = (−b ± √D)/(2a). For two real roots, a stable equivalent uses q = −(b + sign(b)√D)/2, then roots q/a and c/q.

Assumptions & limitations

a must be nonzero; a=0 is a linear equation and is not solved here. Real roots are displayed; complex roots are identified but not formatted. Very small coefficient ratios can exceed ordinary floating-point precision.

Worked example

For a=1, b=−3, c=2, D=9−8=1 and roots are 1 and 2. For a=1, b=2, c=1, D=0 and the repeated root is −1. For a=1, b=0, c=1, D=−4 and there are no real roots.

Common questions