Algebra
Intermediate

Discriminant

Determines the nature of the roots of a quadratic equation.

Formula

Δ=b2−4ac\Delta = b^2 - 4ac

Variables

a,b,cCoefficients of the quadratic

Example

Δ > 0: two real roots; Δ = 0: one root; Δ < 0: complex roots

Did You Know?

The single sign of the discriminant tells you the whole story: positive means two real roots, zero means one, negative means the roots are imaginary.

quadraticdiscriminantroots