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

Question

Accepted Answer

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

$$ \Rightarrow $$ $$9{x^2} - 15\left| x \right| - 3\left| x \right| + 5 = 0$$ ($$ \because $$ x2 = $${\left| x \right|^2}$$)

$$ \Rightarrow $$ $\left| x \right| = {1 \over 3},\,{5 \over 3}$$ \Rightarrow $$x =  \pm {1 \over 3}, \pm \,{5 \over 3}$$ \therefore $Product of roots

=$\left( \frac{1}{3} \right)  \left( -\frac{1}{3} \right)  \left( \frac{5}{3} \right)  \left( -\frac{5}{3} \right)  $=${{25} \over {81}}$

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