Discriminant Calculator

About this calculator

The discriminant of a quadratic equation ax² + bx + c = 0 is Δ = b² − 4ac, the expression that sits under the square root in the quadratic formula. Its sign alone tells you how many real solutions the equation has without solving it fully: a positive discriminant means two distinct real roots, a discriminant of exactly zero means one repeated real root (the parabola just touches the x-axis), and a negative discriminant means no real roots, only a pair of complex conjugate solutions.

Algebra and precalculus students and teachers use the discriminant to quickly check how many times a parabola crosses the x-axis before graphing it, and it shows up again in physics and engineering whenever a quadratic model — projectile motion, circuit equations, optimization problems — needs to be checked for whether a real solution exists at all.

This calculator takes the coefficients a, b, and c of your quadratic equation and returns the discriminant along with how many real roots the equation has.