Polynomial Roots Calculator

What this calculator solves

This calculator finds the roots (solutions) of a quadratic equation written in the standard form ax² + bx + c = 0. A quadratic can have two real roots, one repeated real root, or two complex roots, depending on its coefficients.

The formula used

The quadratic formula is x = (-b ± √(b² – 4ac)) / (2a). The value under the square root, called the discriminant (b² – 4ac), determines the type of roots: positive gives two distinct real roots, zero gives one repeated real root, and negative gives two complex conjugate roots, shown here as a real part and an imaginary part.

This tool is intended for general math and engineering learning purposes.