Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 1 - 1.6 - Other Types of Equations - 1.6 Exercises - Page 128: 9


-3i, 3i, 3, -3

Work Step by Step

Equation : $x^{4}-81=0$ $x^{4}-81=x^{4}-3^4=(x^2-3^2)(x^2+3^2)=(x^2-3^2)(x^2-(3i)^2)=0$ (as $i^2=-1$) Hence, $x^{4}-81=(x-3)(x+3)(x-3i(x+3i)=0$ Giving us 4 roots as 3, -3, 3i, -3i.
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