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 379: 81

Answer

The graph is shown below:
1569487458

Work Step by Step

The polynomial function is, $f\left( x \right)=3{{x}^{4}}+4{{x}^{3}}-7{{x}^{2}}-2x-3$ The degree of the polynomial function is $4$. From the above graph it can be seen that the function $f\left( x \right)$ cut the horizontal axis $\left( x-\text{axis} \right)$ at two points. That means the number of real roots of the function is $2$. The number of imaginary roots of the function is equal to the difference between the degree of the function and the number of real roots. Therefore, the number of imaginary root is, $\begin{align} & \left( \text{degree}\text{of}\ \text{the}\ \text{function} \right)-\left( \text{number}\ \text{of}\ \text{real}\ \text{root} \right)=4-2 \\ & =2 \end{align}$
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.