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: 59


$x=\frac{2}{3},-1\pm\sqrt 2$

Work Step by Step

Step 1. For $3x^3+4x^2-7x+2=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2,\pm\frac{1}{3},\pm\frac{2}{3}$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=\frac{2}{3}$. Step 3. Use the quotient to find other zeros: $3x^2+6x-3=0 \Longrightarrow x^2+2x-1=0 \Longrightarrow x=\frac{-2\pm\sqrt {4-4(-1)}}{2}=-1\pm\sqrt 2$
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