Question

If $h\left(x\right)=5-9x$ and $h^{-1}\left(x\right)$ is obtained in the form $\frac{b-ax}{9}$, then the quadratic equation with roots $a$ and $b$ is

• A. $x^2-6x+5=0$
• B. $x^2+6x+5=0$
• C. $x^2-6x-7=0$
• D. $x^2-7x+10=0$

Answer 1

The correct option is A $x^2-6x+5=0$

Let $y=5-9x$
$\Rightarrow 9x=5-y\Rightarrow x=\frac{5-y}{9}$
Replace $x$ and $y$
$\Rightarrow y=\frac{5-x}{9}\Rightarrow h^{-1}\left(x\right)=\frac{5-x}{9}$
Comparing with $\frac{b-ax}{9}$ form, we have
$a=1;b=5$
$\therefore$ The required quadratic will be of the form
$k(x-1)(x-5)=0\Rightarrow k(x^2-6x+5)=0$
So, from the given options the quadratic equation is
$x^2-6x+5=0$