Question:
The product of the roots of the equation $9 x^{2}-18|x|+5=$ 0 , is :
Correct Option: , 2
Solution:
Let $|x|=y$ then
$9 y^{2}-18 y+5=0$
$\Rightarrow 9 y^{2}-15 y-3 y+5=0$
$\Rightarrow(3 y-1)(3 y-5)=0$
$\Rightarrow y=\frac{1}{3}$ or $\frac{5}{3} \Rightarrow|x|=\frac{1}{3}$ or $\frac{5}{3}$
Roots are $\pm \frac{1}{3}$ and $\pm \frac{5}{3}$
$\therefore$ Product $=\frac{25}{81}$