College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 387: 22


Maximum number of zeros: $4.$ 1 positive, 1 negative zero.

Work Step by Step

$(-x)^{n}=\left\{\begin{array}{ll} x^{n} & \text{if n is even}\\ -x^{n} & \text{if n is odd} \end{array}\right.$ --- $f(x)=5x^{4}+2x^{2}-6x-5$ has 1 change in signs, from $+2x^{2}$ to $-6x$. By Descartes’ Rule of Signs, f has 1 positive zero. $f(-x)=5x^{4}+2x^{2}+6x-5$ has 1 change in signs, so it has 1 negative zero. The degree of the polynomial is 4, which is the maximum number of zeros.
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