Quadratic Equation Solver

The quadratic formula solves ax² + bx + c = 0 for x: x = (−b ± √(b² − 4ac)) / (2a). The term b² − 4ac is called the discriminant, and its sign determines whether the equation has two real roots, one repeated real root, or two complex roots.

A positive discriminant means two distinct real roots. A discriminant of exactly zero means one repeated real root (the parabola touches the x-axis at a single point). A negative discriminant means the roots are complex numbers, meaning the parabola never crosses the x-axis.