College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 3, Polynomial and Rational Functions - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises: 7

Answer

(a) $\left\{0, -2i, 2i\right\}$. (b) $P(x) = x^2(x-2i)(x+2i)$

Work Step by Step

$\bf{(a) \text{ Zeros}}$ Factor the polynomial completely to obtain: $P(x) = x^2(x^2+4) \\P(x) = x^2(x-2i)(x+2i)$ Equate each factor to zero then solve each equation to obtain: \begin{array}{ccccc} &x^2=0 &\text{or} &x-2i=0 &\text{or} &x+2i=0 \\&x=0 &\text{or} &x=2i &\text{or} &x=-2i \end{array} Thus, the zeros of the function are: $\left\{0, -2i, 2i\right\}$. $\bf{(b) \text{ Completely Factored Form}}$ From part (a) above, the completely factored form of $P(x)$ is: $P(x) = x^2(x-2i)(x+2i)$
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.