For the quadratic ax² + bx + c = 0, the quantity b²−4ac is the discriminant. The quadratic has two distinct real roots, repeated roots, or no real roots according to whether the discriminant is positive, zero, or negative.

Note the quadratic’s discriminant equals a²(α‎–β‎)² where α‎ and β‎ are the quadratic’s root. The discriminant of the cubic ax³ + bx² + cx + d = 0 equals a⁴(α‎–β‎)²(β‎–γ‎)²(γ‎–α‎)² where α‎,β‎,γ‎ are the cubic’s roots, and higher degree polynomials have similarly defined discriminants.