Exercises 72 and 73: A basic fact of algebra states that c is a root of a
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Exercises 72 and 73: A basic fact of algebra states that c is a root of a polynomial ƒ if and only if ƒ(x) = (x − c)g(x) for some polynomial g. We say that c is a multiple root if ƒ(x) = (x − c)^{2}h(x), where h is a polynomial.
Show that c is a multiple root of ƒ if and only if c is a root of both ƒ and ƒ'.
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Assume first that f c f c 0 and let us show that c is a multiple root of f x We have f x x c ...View the full answer
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