Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 377: 16

Answer

a. $\frac{p}{q}=\pm1,\pm5$ b. $x=1$; see figure. c. $x=1,\frac{3\pm i\sqrt {11}}{2}$
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Work Step by Step

a. Given the function $f(x)=x^3-4x^2+8x-5$, we have $p=\pm1,\pm5$ and $q=\pm1$. Thus the possible rational zeros are $\frac{p}{q}=\pm1,\pm5$ b. Starting from the easiest number, test the possible rational zeros using synthetic division. We can find $x=1$ as a zero (shown in the figure). c. Based on the results from part-b, we have $f(x)=x^3-4x^2+8x-5=(x-1)(x^2-3x+5)$ Thus the zeros are $x=1,\frac{3\pm i\sqrt {11}}{2}$
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