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: $ax^{2} + bx + c = 0$ is $b^{2} - 4ac$.
The discriminant of the cubic equation: $x^{3} + qx + r = 0$ is $4q^{3} + 27r^{2}$.

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.