Figure 7 is the graph of a polynomial with roots at A, B, and C. Which of

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Figure 7 is the graph of a polynomial with roots at A, B, and C. Which of these is a multiple root? Explain your reasoning using Exercise 72.

A B FIGURE 7 C X


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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