# 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

- Serge Lang (1993).
*Algebra*, 3rd ed. Addison-Wesley, 193-194,204-205,325-326. ISBN 0-201-55540-9.