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. $\frac{25}{9}$

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

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

  4. $\frac{5}{9}$


Correct Option: , 2

Solution:

$9 x^{2}-18|x|+5=0$

$9|x|^{2}-15|x|-3|x|+5=0\left(\because x^{2}=|x|^{2}\right)$

$3|x|(3|x|-5)-(3|x|-5)=0$

$|x|=\frac{1}{3}, \frac{5}{3}$

$x=\pm \frac{1}{3}, \pm \frac{5}{3}$

Product of roots $=\frac{25}{81}$

 

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