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: 15


1, -1 , $\frac{1+i\sqrt3}{2}$, $\frac{1-i\sqrt3}{2}$

Work Step by Step

$x^4-x^3+x-1=x^3(x-1)+1(x-1)=(x^3+1)(x-1)=0$ $(x+1)(x^2-x+1)(x-1)=0$ Either x+1=0 giving x=-1 or x-1=0 giving x=1 or $x^2-x+1=0$ giving x = $\frac{1+i\sqrt3}{2}$ or $\frac{1-i\sqrt3}{2}$ (using the discriminant formula for roots of the quadratic equation, x = $ \frac{-b+\sqrt{b^2-4ac}}{2a}$ or $ \frac{-b-\sqrt{b^2-4ac}}{2a}$)
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