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?