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: 89

Answer

$x=1.15$

Work Step by Step

We test $f(x)=x^{3}+x^{2}+x-4$ on nonnegative integer values of x, and find that $f(1) $is negative, $f(2)$is positive $\Rightarrow$ by the IVT, a real zero is inside $[1,2].$ Subdividing $[1,2]$ into 10 subintervals, calculating f( endpoints), we find $f(1.1) $is negative, $f(1.2)$is positive $\Rightarrow$ by the IVT, a real zero is inside $[1.1,1.2].$ Subdividing again, we find $f(1.15) $is negative, $f(1.16)$is positive $\Rightarrow$ by the IVT, a real zero is inside $[1.15,1.16].$ The real zero is $x=1.15...$ To two decimal places, $x=1.15$
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