Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.5 The Real Zeros of a Polynomial Function - 4.5 Assess Your Understanding - Page 233: 49

Answer

$\{2, \pm \sqrt 5 \}$, $f(x)=2(x-2)(x+\sqrt 5)(x-\sqrt 5)$

Work Step by Step

Step 1. Given $f(x)=2x^3-4x^2-10x+20$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\frac{1}{2},\pm\frac{5}{2}$ Step 2. Use synthetic division as shown in the figure to find one zero $x=2$. Step 3. Use the quotient to solve $2x^2-10=0$ or $x^2=5$, thus $x=\pm \sqrt 5$ Step 4. Thus the real zeros are $\{2, \pm \sqrt 5 \}$ and we can factor the function as $f(x)=2(x-2)(x+\sqrt 5)(x-\sqrt 5)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.