Discriminant of a polynomial: Difference between revisions

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In [[algebra]], the '''discriminant of a polynomial''' is an invariant which determines whether or not the polynomial has repeated roots.
In [[algebra]], the '''discriminant of a polynomial''' is an invariant which determines whether or not a [[polynomial]] has repeated roots.


Given a polynomial
Given a polynomial

Revision as of 01:31, 18 December 2008

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 derivative.

Examples

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