A discriminant is a number, usually invariant under suitable transformations, which characterizes some properties of the roots of a certain quantity.

For instance, the most common application of the concept of discriminant is in the second-degree equation a x² + b x+ c=0.

In this context, the discriminant is the quantity D= b²- 4a c. According to the sign of D, such an equation can have either two distinct roots (if D is greater than zero), or only one root (in the case D=0), or no root (if D is less than zero).

The concept of discriminant is also used for polynomials. In the case of a polynomial with real coefficients, the discriminant is defined as the product of the squares of the differences of the complex roots. Since the non-real roots of such a polynomial are in conjugated pairs, the discriminant is a real number. Moreover, the...