Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - 3.3 Zeros of Polynomial Functions - 3.3 Exercises - Page 337: 91

Answer

See table.

Work Step by Step

Step 1. Given $f(x)=5x^6-6x^5+7x^3-4x^2+x+2$, we can identify 4 sign changes indicating that there could be 4, 2 or 0 positive zeros. Put the numbers in the table. Step 2. $f(-x)=5x^6+6x^5-7x^3-4x^2-x+2$, we can identify 2 sign changes indicating that there could be 2 or 0 negative zeros. Put the numbers in the table. Step 3. There should be 6 total zeros. thus the number of nonreal zeros will be the remaining after taking real zeros into account. Complete the table as shown.
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