discriminant The discriminant of a polynomial equation is a function of the coefficients which allows one to say when it has a pair of equal roots.
The discriminant of the quadratic equation: ax² + bx + c = 0 is b² - 4ac.
The discriminant of the cubic equation: x³ + qx + r = 0 is 4q³ + 27r².

The discriminant of an algebraic number field is an important numerical invariant that (roughly) measures the size of the ring of integers of the field.