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 - 11.5 Equations Reducible to Quadratic - 11.5 Exercise Set - Page 731: 1


True statement

Work Step by Step

$a{{x}^{2}}+bx+c=0$ Any other trinomial of the form $d{{x}^{m}}+e{{x}^{n}}+f=0$ (where m and n are integers and $n\ne 0$) can be reduced to quadratic form if $m=2n$ by substituting ${{x}^{n}}=u$. $\begin{align} & d{{x}^{m}}+e{{x}^{n}}+f=0 \\ & d{{\left( {{x}^{n}} \right)}^{2}}+e\left( {{x}^{n}} \right)+f=0 \\ & d{{u}^{2}}+eu+f=0 \end{align}$ $d{{u}^{2}}+eu+f=0$ is the reduced quadratic form of $d{{x}^{m}}+e{{x}^{n}}+f=0$. Thus, the given statement is true.
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