Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Test: 3

Answer

$x_{1}=\dfrac{1 + \sqrt{31}i}{2}$ and $x_{2}=\dfrac{1- \sqrt{31}i}{2}$

Work Step by Step

Given $m^2-m+8=0$ $a=1, \ b=-1, \ c=8$ Using the quadratic formula: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a} , $ we have: $\dfrac{-(-1)\pm \sqrt{(-1)^2-4\times 1\times 8}}{2\times 1} = \dfrac{1\pm \sqrt{1-32}}{2} = \dfrac{1\pm \sqrt{-31}}{2} = \dfrac{1\pm \sqrt{31}i}{2}$ Therefore the solutions are $x_{1}=\dfrac{1 + \sqrt{31}i}{2}$ and $x_{2}=\dfrac{1- \sqrt{31}i}{2}$
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