Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 67


$x=\frac{1}{2}, 5$, $x=2$ (multiplicity 2).

Work Step by Step

Step 1.For $2x^4-19x^3+57x^2-64x+20=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\frac{1}{2},\pm\frac{5}{2}$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=2,5$ Step 3. Use the quotient to find other zeros: $2x^2-5x+2=0 \Longrightarrow (2x-1)(x-2)=0 \Longrightarrow x=\frac{1}{2}, 2$
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