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 - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 714: 69

Answer

$\frac{1}{2}$

Work Step by Step

$k{{x}^{2}}+3x-k=0$ Substitute $x=-2$ to get the value of k as shown below, $\begin{align} & k{{\left( -2 \right)}^{2}}+3\left( -2 \right)-k=0 \\ & 4k-6-k=0 \\ & 3k=6 \\ & k=\frac{6}{3} \end{align}$ Simplify, $k=2$ Substitute $k=2$ into the provided equation $k{{x}^{2}}+3x-k=0$, $2{{x}^{2}}+3x-2=0$ Now compare the equation $2{{x}^{2}}+3x-2=0$ with the standard form of the quadratic equation $a{{x}^{2}}+bx+c=0$, Here, $a=2,b=3$ and $c=-2$ Substitute $a=2,b=3$ and $c=-2$ into the quadratic formula $x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$, $\begin{align} & x=\frac{-3\pm \sqrt{{{3}^{2}}-4\left( 2 \right)\left( -2 \right)}}{2\left( 2 \right)} \\ & =\frac{-3\pm \sqrt{9+16}}{4} \\ & =\frac{-3\pm \sqrt{25}}{4} \\ & =\frac{-3\pm 5}{4} \end{align}$ Simplify more, $\begin{align} & x=\frac{-3+5}{4} \\ & =\frac{2}{4} \\ & =\frac{1}{2} \end{align}$ And, $\begin{align} & x=\frac{-3-5}{4} \\ & =\frac{-8}{4} \\ & =-2 \end{align}$
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