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

Question

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

Accepted Answer

Let $y=|x|$: $9y^2-18y+5=0 \implies (3y-1)(3y-5)=0 \implies y=\dfrac13,\dfrac53$.

Roots: $x=\pm\dfrac13,\pm\dfrac53$. Product $=\dfrac13\cdot\left(-\dfrac13\right)\cdot\dfrac53\cdot\left(-\dfrac53\right)=\dfrac{25}{81}.$

Solutions · 1