College Algebra (10th Edition)

Published by Pearson

Chapter 8 - Section 8.7 - Systems of Inequalities - 8.7 Assess Your Understanding - Page 625: 64

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. $f(-1)=6\cdot(-1)^2+5(-1)-6=6-5-6=-5.$ $f(2)=6\cdot(2)^2+5(2)-6=24+10-6=28.$ Since $-1\lt0\lt10$, according to the Intermediate Value Theorem, there must be a $0$ in the given interval.

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