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: 80


See below.

Work Step by Step

The Intermediate Value Theorem says that if a continuous (polynomials are always continuous) function on an interval [a,b] takes values $f(a)$ and $f(b)$ at the endpoints, then the function takes all values between $f(a)$ and $f(b)$ at some point of the interval. Evaluate the function at the endpoints. $f(-1)=(-1)^4+8\cdot(-1)^3-(-1)^2+2=1-8-1+2=-6.$ $f(0)=(0)^4+8\cdot(0)^3-(0)^2+2=0-0+0+2=2.$ Since $-6\lt0\lt2$, according to the Intermediate Value Theorem, there must be a $0$ in the given interval.
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