Quadratic equation solver

Formula & example

Enter a, b and c for ax² + bx + c = 0. The discriminant b² − 4 ac determines two real roots, one repeated root or a complex conjugate pair. Rational roots are exact; irrational roots keep their radical expression and show an approximation. Substitution checks for approximate real roots use a scaled residual, which measures numerical error rather than proving a symbolic identity. If a is zero, the solver handles the remaining linear equation. Example: x² − 3 x + 2 = 0 gives 1 and 2; x² + 1 = 0 gives ±i.

ax² + bx + c = 0; D = b² − 4 ac

x² − 3 x + 2 = 0 → x = 1, 2