Quadratic Equation - Nature of roots

Question

What is the product of real roots of the equation $t^2x^2+|x|+q=0$

Since the complex equation is positive so sum of the roots are positive, here I am having four option as answers :

1. $>0$
2. $<0$
3. not exist
4. irrelevant

Answer 1

If $q>0$ there are no real roots. If $q=0$ there is only one real root: $x=0$. Let's see what happens if $q<0$. The left hand side of the equation is even (that is, it does not change if we change $x$ by $-x$). This implies that if $a$ is a root of the equation, so is $-a$. Then the product of the roots is ...