Question

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

• A. is always positve
• B. is always negative
• C. does not exists
• D. none of these

Answer 1

The correct option is C does not exists

Here in the above question we have equation $t^2{x}^2+|x|+9$ where, obviously $t^2{x}^2$ is greater than equal to zero, also |x| is greater than zero and 9 ia also a positive number so it's also greater than zero. So, on adding these inequalities we get $t^2{x}^2+|x|+9$ as always greater than zero as long as t and x are assumed real, hence no real roots exist. Therefore product of real roots of the above given equation does not exists.