Answer
$x^3+4x=0$
Work Step by Step
A polynomial equation that has solutions $\{0,2i,-2i\}$ is
\begin{array}{l}\require{cancel}
x(x+2i)(x-2i)=0
\\\\
x(x^2-4i^2)=0
\\\\
x(x^2-4(-1))=0
\\\\
x(x^2+4)=0
\\\\
x^3+4x=0
.\end{array}
Intermediate Algebra (6th Edition)
by Martin-Gay, Elayn
Published by
Pearson
ISBN 10:
0321785045
ISBN 13:
978-0-32178-504-6
Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 504: 88
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