Question

Product of real roots of the equation $t^2{x}^2+|x|+9=0$

• A. is always positive
• B. is always negative
• C. does not exist
• D. none of these

Answer 1

The correct option is C does not exist

$t^2{x}^2+|x|+9=0$

Now $t^2$ always $\ge 0$ __(1)

and $t^2{x}^2$ always $\ge 0$ __(2)

$|x|$ always $\ge 0$ as $|-ve|=+ve$ __(3)

$a>0$ __(4)

Now Adding (2), (3), (4) will always give value greater than 0 and never equal to 0.

$\therefore$ No real root exist for the given equation.