Chapter 4 - Polynomial and Rational Functions - 4.5 The Real Zeros of a Polynomial Function - 4.5 Assess Your Understanding - Page 234: 83

See explanations.

Step 1. Given $f(x)=x^5-x^4+7x^3-7x^2-18x+18$, we have $f(1.4)=(1.4)^5-(1.4)^4+7(1.4)^3-7(1.4)^2-18(1.4)+18\approx-0.18\lt0$ Step 2. Similarly, we have $f(1.5)=(1.5)^5-(1.5)^4+7(1.5)^3-7(1.5)^2-18(1.5)+18\approx1.41\gt0$ Step 3. Based on the Intermediate Value Theorem, there is a zero in the given interval.