Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Review Exercises - Page 431: 61

Answer

$f(x)= x^3-6x^2+21x-26$ See graph.
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Work Step by Step

Step 1. Given the zeros as $2$ and $2-3i$, we can identify all the zeros as $x=2, 2\pm3i$ Step 2. As $n=3$, we can write the polynomial as $f(x)=(x-2)(x-2-3i)(x-2+3i)=(x-2)((x-2)^2+9)=(x-2)(x^2-4x+13)=x^3-4x^2+13x-2x^2+8x-26=x^3-6x^2+21x-26$ Step 3. Letting $x=1$, we have $f(1)=1-6+21-26=-10$ Step 4. See graph for zeros and $f(1)$
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