College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Review Exercises: 40

Answer

$\displaystyle x=-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$

Work Step by Step

We are given: $x^{2}+x+1=0$ We solve using the quadratic formula ($a=1,\ b=1,\ c=1$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-1\pm\sqrt{1^{2}-4*1*1}}{2(1)}$ $\displaystyle x=\frac{-1\pm\sqrt{1-4}}{2(1)}$ $\displaystyle x=\frac{-1\pm\sqrt{-3}}{2(1)}$ $\displaystyle x=\frac{-1\pm\sqrt{3}i}{2}$ $\displaystyle x=-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i$
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