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 - Concept and Vocabulary Check: 8



Work Step by Step

Descartes's Rule of Signs (page 384) Let $f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{2}x^{2}+a_{1}x+a_{0}$ be a polynomial with real coefficients. 1. 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. 2. The number of NEGATIVE ... --------------------------- With four sign changes the number of positive zeros can be (a) 4 or (b) 2, or 0 "must have four" is false, there may be less.
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