# 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.