The product of the roots of the equation 9x^{ | vedclass

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(B) Given equation: $9x^{2}-18|x|+5=0$Since $x^{2} = |x|^{2}$,the equation becomes $9|x|^{2}-18|x|+5=0$.Let $t = |x|$,then $9t^{2}-18t+5=0$.Factoring

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$\frac{25}{81}$

Vedclass · Answer

(B) Given equation: $9x^{2}-18|x|+5=0$Since $x^{2} = |x|^{2}$,the equation becomes $9|x|^{2}-18|x|+5=0$.Let $t = |x|$,then $9t^{2}-18t+5=0$.Factoring the quadratic: $9t^{2}-15t-3t+5=0$.$3t(3t-5)-1(3t-5)=0$.$(3t-1)(3t-5)=0$.So,$|x| = \frac{1}{3}$ or $|x| = \frac{5}{3}$.The roots are $x = \frac{1}{3}, -\frac{1}{3}, \frac{5}{3}, -\frac{5}{3}$.The product of the roots is $(\frac{1}{3}) 	imes (-\frac{1}{3}) 	imes (\frac{5}{3}) 	imes (-\frac{5}{3}) = \frac{25}{81}$.

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

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