Quadratic Equation Calculator

A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0. It can have two real roots, one repeated root, or two complex (imaginary) roots, depending on the discriminant (b² − 4ac).

x = (−b ± √(b² − 4ac)) / (2a). The ± means there are generally two solutions (roots). The part under the square root, b² − 4ac, is called the discriminant.

If b² − 4ac > 0: two distinct real roots. If b² − 4ac = 0: one repeated real root. If b² − 4ac < 0: two complex conjugate roots (no real solutions).

The vertex is the highest or lowest point of the parabola. Its x-coordinate is −b/(2a) and the y-coordinate is found by substituting this into the equation. If a > 0, the parabola opens upward; if a < 0, downward.

Quadratic equations appear in multiple WAEC Additional Mathematics and JAMB questions every year. Understanding how to derive roots using the formula, completing the square, and factorisation is essential for achieving high scores.