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.
The discriminant of a quadratic is , which plays a key part in the solution of the quadratic equation.
- Serge Lang (1993). Algebra, 3rd ed. Addison-Wesley, 193-194,204-205,325-326. ISBN 0-201-55540-9.