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

$a{{x}^{2}}+bx+c=0$ 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.