Algebra: A Combined Approach (4th Edition)

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

Chapter 11 - Section 11.3 - Integrated Review - Summary on Solving Quadratic Equations: 13

Answer

$x_{1}= -\dfrac{3}{2} + \dfrac{\sqrt{15}i}{2}$ and $x_{2} = -\dfrac{3}{2} - \dfrac{\sqrt{15}i}{2}$

Work Step by Step

Given $x^2+3x+6=0$ $a= 1, \ b=3, \ c=6$ Using the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ we have: $\dfrac{-3 \pm \sqrt{3^2-4 \times 1\times 6}}{2 \times 1} = \dfrac{-3 \pm \sqrt{9-24}}{2} = \dfrac{-3 \pm \sqrt{-15}}{2} = \dfrac{-3 \pm \sqrt{15}i}{2} = -\dfrac{3}{2} \pm \dfrac{\sqrt{15}i}{2}$ Therefore the solutions are $x_{1}= -\dfrac{3}{2} + \dfrac{\sqrt{15}i}{2}$ and $x_{2} = -\dfrac{3}{2} - \dfrac{\sqrt{15}i}{2}$
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