Problem #PRU-61018

Problems Calculus Derivative Derivative and multiple roots Algebra and arithmetic Polynomials Polynomial remainder theorem (little Bezout's theorem). Factorisation.
 15–16  3.0

Problem

Prove that the root a of the polynomial \(P (x)\) has multiplicity greater than 1 if and only if \(P (a) = 0\) and \(P '(a) = 0\).