A discriminant is a quantity that gives valuable information about the solutions of an equation. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is given by d = b2 - 4ac. 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.