Question: Let f(x) be a polynomial. Suppose on an interval [a, b], f(x) has a double root at x=a and a double root at x=b. Prove

Let f(x) be a polynomial. Suppose on an interval [a, b], f(x) has a double root at x=a and a double root at x=b. Prove f'(x) has at least three roots in [a, b].

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