# discriminant

A discriminant is a quantity that gives valuable information about the solutions of an equation.
In the case of a quadratic equation *ax*^{ 2} + *bx* + *c* = 0, the discriminant is given by*D* = *b*^{ 2} – 4*ac*. If* D *> 0, the roots of
the equation are two different real numbers;
if* D *= 0, the roots are real and equal; if* D* < 0, the
roots are complex numbers. The concept
of discriminant can also be applied in the case of polynomials, elliptic curves, and metrics.