Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 4 - Section 4.1 - Angles and Radian Measure - Exercise Set - Page 534: 125


The required solution is $\left\{ -2\pm i\sqrt{2} \right\}$

Work Step by Step

We have to write the general form of a quadratic equation: $a{{x}^{2}}+bx+c=0$ Write the given equation: ${{x}^{2}}+4x+6=0$ Identify the values of $a$ , $b$ , and $c$. Thus, $a=1$ , $b=4$ , and $c=6$. Use the following quadratic formula: $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ Put $1$ for $a$, $4$ for $b$, and $6$ for $c$: $\begin{align} & x=\frac{-4\pm \sqrt{{{\left( 4 \right)}^{2}}-4\left( 1 \right)\left( 6 \right)}}{2\left( 1 \right)} \\ & =\frac{-4\pm \sqrt{16-24}}{2} \\ & =\frac{-4\pm \sqrt{-8}}{2} \\ & =\frac{-4\pm i2\sqrt{2}}{2} \end{align}$ Solve further, $x=-2\pm i\sqrt{2}$ Hence, the solution is $\left\{ -2\pm i\sqrt{2} \right\}$.
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