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 - Page 329: 8


(a) $\left\{0, -3i, 3i\right\}$. (b) $P(x) = x^3(x-3i)(x+3i)$

Work Step by Step

$\bf{(a) \text{ Zeros}}$ Factor the polynomial completely to obtain: $P(x) = x^3(x^2+9) \\P(x) = x^3(x-3i)(x+3i)$ Equate each factor to zero then solve each equation to obtain: \begin{array}{ccccc} &x^3=0 &\text{or} &x-3i=0 &\text{or} &x+3i=0 \\&x=0 &\text{or} &x=3i &\text{or} &x=-3i \end{array} Thus, the zeros of the function are: $\left\{0, -3i, 3i\right\}$. $\bf{(b) \text{ Completely Factored Form}}$ From part (a) above, the completely factored form of $P(x)$ is: $P(x) = x^3(x-3i)(x+3i)$
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.