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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
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1 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 ...

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but the answer it is given is irrelevant... and as per your details the answer is $-a^2$ –  Sachin Sharmaa Mar 21 '13 at 16:40
    
And thus is $<0$. –  Julián Aguirre Mar 21 '13 at 17:23

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