Posted by **t** on Tuesday, September 27, 2011 at 3:24pm.

A basic fact of algebra states that c is a root of a polynomial f(x) if and only if f(x) = (x-c)g(x) for some polynomial g(x). We say that c is a multiple root if f(x) = [(x-c)^2](h(x)) where h(x) is a polynomial.

Show that c is a multiple root of f(x) if and only if c is a root of both f(x) and f'(x)

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