College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.5 - Complex Numbers - 1.5 Exercises - Page 131: 72


$\displaystyle -\frac{1}{4}\pm\frac{\sqrt{15}}{4}i$

Work Step by Step

$\displaystyle x^{2}+\frac{1}{2}x+1=0$ We use the quadratic formula ($a=1, b=1/2, c=1$): $x=\displaystyle \frac{-\frac{1}{2}\pm\sqrt{(\frac{1}{2})^{2}-4*1*1}}{2(1)}=\frac{-\frac{1}{2}\pm\sqrt{\frac{1}{4}-\frac{16}{4}}}{2}=\frac{-\frac{1}{2}\pm\sqrt{-\frac{15}{4}}}{2}=\frac{-\frac{1}{2}\pm\frac{1}{2}\sqrt{15}i}{2}=-\frac{1}{4}\pm\frac{\sqrt{15}}{4}i$
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