College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.4 - Page 388: 67

Answer

please see "step by step"

Work Step by Step

(see page 384) For estimating the possible number of POSITIVE zeros, we count the number of sign changes in the defining expression of the polynomial, $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{2}x^{2}+a_{1}x+a_{0}$ where the coefficients are real numbers. The number of positive real zeros of $f$ is either $\mathrm{a}$. the same as the number of sign changes of $f(x)$ or $\mathrm{b}$. less than the number of sign changes of $f(x)$ by a positive even integer. If $f(x)$ has only one variation in sign, then $f$ has exactly one positive real zero.
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