Quadratic Equation Solver

About Quadratic Equations

A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0. The solutions (roots) are found using the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a.

The discriminant (Δ = b² − 4ac) determines the nature of the roots. When Δ > 0, there are two distinct real roots. When Δ = 0, there is exactly one repeated root. When Δ < 0, the roots are complex conjugates involving the imaginary unit i.

The graph of a quadratic function is a parabola. If a > 0 it opens upward; if a < 0 it opens downward. The vertex is the turning point, located at x = −b/2a.