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 388: 88

Answer

$x=-2.17$

Work Step by Step

$f(x)=3x^{3}-10x+9=0$ Work shown in image below. Subdivide the interval $[-3,-2]$ into 10 subintervals and find f(each endpoint). We find opposite signs on endpoints of $[-2.2,-2.1 ]$. By the Intermediate Value Theorem, a real zero is inside that interval. Subdivide the interval $[-2.2,-2.1 ]$ into 10 subintervals and find f(each endpoint). We find opposite signs on endpoints of $[-2.18,-2.17]$. So a real zero is $x=-2.17...$ Correct to 2 decimal places : $x=-2.17$
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