Question

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

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

The given Quadratic Equation is

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

So we can rewrite the above equation in below two equations as :

$9 {x}^{2} - 18x + 5 = 0 \: \: \: ...(1)$

And

$9 {x}^{2} + 18x + 5 = 0 \: \: \: ...(2)$

Now

FROM EQUATION 1

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

$\implies \: 9 {x}^{2} - 15x - 3x + 5 = 0$

$\implies \: 3x(3x - 5) - 1 \times (3x - 5) = 0$

$\implies \:(3x - 5)(3x - 1) = 0$

$\implies \: \displaystyle \: x = \frac{5}{3} \: , \: \frac{1}{3}$

So the roots are

$\: \displaystyle \: \frac{5}{3} \: , \: \frac{1}{3}$

FROM EQUATION 2

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

$\implies \: 9 {x}^{2} + 15x + 3x + 5 = 0$

$\implies \: 3x(3x + 5) + 1 \times (3x + 5) = 0$

$\implies \:(3x + 5)(3x + 1) = 0$

$\implies \: \displaystyle \: x = - \frac{5}{3} \: , \: - \frac{1}{3}$

So the roots are

$\displaystyle \: - \frac{5}{3} \: , \: - \frac{1}{3}$

Hence the required product of all roots are

$= \: \displaystyle \: \frac{5}{3} \: \times \: \frac{1}{3} \times ( - \frac{5}{3} \: ) \: \times ( - \: \frac{1}{3} \: )$

$= \displaystyle \: \frac{25}{81}$

Answer 2

Answer:

A is the correct answer

Step-by-step explanation:

please mark as brainliest answer