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.