The product of the roots of the
equation 9x² - 18|x| + 5 = 0 is :

$9{x^2} - 18\left| x \right| + 5 = 0$<br><br>$\Rightarrow$ $9{x^2} - 15\left| x \right| - 3\left| x \right| + 5 = 0$ ($\because$ x² = ${\left| x \right|^2}$)<br><br>$\Rightarrow$ $3\left| x \right|(3\left| x \right| - 5) - (3\left| x \right| - 5) = 0$<br><br>$\Rightarrow$$\left| x \right| = {1 \over 3},\,{5 \over 3}$<br><br>$\Rightarrow$ $x = \pm {1 \over 3}, \pm \,{5 \over 3}$<br><br>$\therefore$ Product of roots <br><br>= $$\left( \frac{1}{3} \right) \left( -\frac{1}{3} \right) \left( \frac{5}{3} \right) \left( -\frac{5}{3} \right) $$ = ${{25} \over {81}}$