The product of the roots of the equation
Question:

The product of the roots of the equation $9 x^{2}-18|x|+5=$ 0 , is :

  1. (1) $\frac{5}{9}$

  2. (2) $\frac{25}{81}$

  3. (3) $\frac{5}{27}$

  4. (4) $\frac{25}{9}$


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 $=\frac{25}{81}$

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