Prove: $x^4+mx^2+x$ have only two roots when $m>0$ I got the question:  

Prove that $x^4+mx^2+x$ have only two roots when $m>0$.

I know that it is a continuous function.
I tried to use solve this question with two steps:  


*

*Use intermediate value theorem to prove that there are at least two roots.

*Use Rolle's theorem to prove that there are not more then two roots.


I am stuck on first step. I can find a positive value of the function, but I can't find $x$ that give me a negative value. I assume that the $x$ that gives the negative value depends on $m$ but we know only that $m>0$, and there are many cases to check.
Any idea how to solve it?

Since the polynomial factors as $x(x^3+mx+1)$, you have one root at $x=0$.  So now you just have to show that $x^3+mx+1$ has exactly one root, and your plan of
action above should do the trick.
