Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.3 Studying Solutions of Quadratic Equations - 11.3 Exercise Set - Page 718: 47



Work Step by Step

$2-7i\ \text{and }2+7i$ It can be expressed as: $x=\text{ }2+7i$ and $x=\text{ }2+7i$ $\begin{align} & x-\left( \text{ }2+7i \right)=0 \\ & \left( x-2 \right)-7i=0 \end{align}$ Or, $\begin{align} & x-\left( 2-7i \right)=0 \\ & \left( x-2 \right)+7i=0 \\ \end{align}$ Apply the zero-product property $\left( \left( x-2 \right)-7i \right)\left( \left( x-2 \right)+7i \right)=0$ $\begin{align} & \left( \left( x-2 \right)-7i \right)\left( \left( x-2 \right)+7i \right)=0 \\ & \left( x-2 \right)\left( x-2 \right)+7i\left( x-2 \right)-7i\left( x-2 \right)-49{{i}^{2}}= \end{align}$ Combine like terms, Here ${{i}^{2}}=1$ which is a complex entry. ${{\left( x-2 \right)}^{2}}-49\left( {{i}^{2}} \right)=0$ Apply the formula, ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ $\begin{align} & {{x}^{2}}+4-4x-49\left( -1 \right)=0 \\ & {{x}^{2}}+4-4x+49=0 \\ & {{x}^{2}}-4x+53=0 \end{align}$
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