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 3.3 Complex Zeros; Fundamental Theorem of Algebra - 3.3 Assess Your Understanding - Page 231: 26

Answer

$-3i,-2,\frac{1}{3}$.

Work Step by Step

Step 1. As $x=3i$ is a zero, we have $x=-3i$ also a zero and $(x-3i)(x+3i)=x^2+9$ is a factor of the function. Step 2. Use synthetic division (two steps) or long division (as shown in the figure) to get the quotient. Step 3. Find other zeros $3x^2+5x-2=0 \Longrightarrow (3x-1)(x+2)=0 \Longrightarrow x=-2,\frac{1}{3}$.
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