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 f 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)2h(x), where h is a polynomial.

Use Exercise 72 to determine whether c = −1 is a multiple root.
(a) x+ 2x4 − 4x3 − 8x2 − x + 2
(b) x+ x3 − 5x2 − 3x + 2


Data From Exercise 72

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)2h(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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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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