The number a is called a double zero (or a zero of multiplicity 2) of the polynomial P if

P(x) = (x -a)^2 q(x) and q(a) not = 0.

Prove that if a is a double zero of P, then a is a zero of both P and P', and P"(a) not = 0.

Recall that a Zero of a polynomial function P is one number a is subset to R such that P(a) = 0. You may assume without proof that q is a polynomial function.

I do not understand the question at all, can anyone explain it and give some hints to prove it?