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: 8


The possible rational zeroes for the function \[f\left( x \right)=4{{x}^{5}}-8{{x}^{4}}-x+2\] are \[\pm 1,\pm 2,\pm \frac{1}{2},\pm \frac{1}{4}\].

Work Step by Step

Here, the constant term is $2$ and the leading coefficient is 4. The factors of the constant term, $2$ are $\pm 1,\pm 2$ and the factors of the leading coefficient, 4 are $\pm 1,\pm 2,\pm 4$. So, the list of all possible rational zeroes is calculated by the formula: $\begin{align} & \text{Possible rational zeroes}=\frac{\text{Factors of the constant term}}{\text{Factors of the leading coefficient}} \\ & =\frac{\text{Factors of }2}{\text{Factors of 4}} \\ & =\frac{\pm 1,\pm 2}{\pm 1,\pm 2,\pm 4} \\ & =\pm 1,\pm 2,\pm \frac{1}{2},\pm \frac{1}{4} \end{align}$ Therefore, there are total eight possible rational zeroes for the function $f\left( x \right)=4{{x}^{5}}-8{{x}^{4}}-x+2$ that are $\pm 1,\pm 2,\pm \frac{1}{2},\pm \frac{1}{4}$.
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