College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding - Page 387: 37


$\pm 2;\pm 1;\pm \dfrac {1}{2};\pm \dfrac {1}{4} $

Work Step by Step

In a polinomial function like $f\left( x\right) =a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots a_{1}x+a_{0}$ If $p/q$, in lowest terms, is a rational zero of $f$, then p must be a factor of $a_0 $ and $q$ must be a factor of $a_n$. Here $f\left( x\right) =-4x^{3}-x^{2}+x+2\Rightarrow a_{n}=-4;a_{0}=2 $ Factors of $a_0$ are $\pm 1,\pm2$ Factors of $a_n$ are $\pm1 , \pm2,\pm4$ So the potential rational zeros are: $\pm 2;\pm 1;\pm \dfrac {1}{2};\pm \dfrac {1}{4} $
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.