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: 85

Answer

$x=0.21.$

Work Step by Step

$f(x)=8x^{4}-2x^{2}+5x-1$ Work shown in image below. Subdivide the interval $[0,1]$ into 10 subintervals and find f(each endpoint). We find opposite signs on endpoints of $[0.2,0.3]$. By the Intermediate Value Theorem, a real zero is inside that interval. Subdivide the interval $[0.2,0.3]$ into 10 subintervals and find f(each endpoint). We find opposite signs on endpoints of $[0.21,0.22]$. So a real zero is $x=0.21...$ Correct to 2 decimal places : $x=0.21.$
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