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: 92

Answer

$x=2.13$

Work Step by Step

We test $f(x)=3x^{3}-2x^{2}-20$ on nonnegative integer values of x, and find that $f(2) $is negative, $f(3)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2,3].$ Subdividing $[2,3]$ into 10 subintervals, calculating f( endpoints), we find $f(2.1) $is negative, $f(2.2)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2.1,2.2].$ Subdividing again, we find $f(2.13) $is negative, $f(2.14)$ is positive $\Rightarrow$ by the IVT, a real zero is inside $[2.53,2.54].$ The real zero is $x=2.13...$ To two decimal places, $x=2.13$
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