In algebra, the discriminant of a polynomial is an invariant which determines whether or not a polynomial has repeated roots.
Given a polynomial
with roots , the discriminant Δ(f) with respect to the variable x is defined as
The discriminant is thus zero if and only if f has a repeated root.
The discriminant may be obtained as the resultant of the polynomial and its formal derivative.
The discriminant of a quadratic is , which plays a key part in the solution of the quadratic equation.