Let f(x) = F[x] be a nonconstant polynomial and a be an element in any field extension E of F. Then, a is a multiple root of

Question

Let f(x) = F[x] be a nonconstant polynomial and a be an element in any field extension E of F. Then, a is a multiple root of f(x) if and only if f(a) = 0 = f'(a); that is, a is a root of both f'(x) and f'(x).

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