Discriminant of a polynomial

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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.

Examples

The discriminant of a quadratic is , which plays a key part in the solution of the quadratic equation.

References