Question

The product of the roots of the equation $9x^2-18\left|x\right|+5=0$ is :

• A. $\frac{25}{9}$
• B. $\frac{5}{9}$
• C. $\frac{25}{81}$
• D. $\frac{5}{27}$

Answer 1

The correct option is C $\frac{25}{81}$

Let $\left|x\right|=t$
$\Rightarrow 9t^2-18t+5=0$
$\Rightarrow 9t^2-15t-3t+5=0$
$\Rightarrow (3t-5)(3t-1)=0$
$\Rightarrow \left|x\right|=\frac{5}{3},\frac{1}{3}$
$\Rightarrow x=\frac{5}{3},\frac{-5}{3},\frac{1}{3},\frac{-1}{3}$
$\Rightarrow$ Product $=\frac{25}{81}$