Let the function h be defined by h(x)=14+$\displaystyle \frac{x^2}{4}$. If h(2m)=9m, what is one possible value of m?
Hello, fabxx!
I assume that is an equal-sign in there . . .
Let: .$\displaystyle h(x)\:=\:14+ \frac{x^2}{4}$.
If $\displaystyle h(2m) \:{\color{red}=}\:9m$, what is one possible value of $\displaystyle m$?
Since $\displaystyle h(2m) \:=\:14 + \frac{(2m)^2}{4} \:=\:14 + m^2$
. . we have: .$\displaystyle 14 + m^2 \:=\:9m \quad\Rightarrow\quad m^2 - 9m + 14 \:=\:0$
Factor:. . $\displaystyle (m - 2)(m - 7) \:=\:0 \quad\Rightarrow\quad\boxed{ m \;=\;2,\;7}$