Math question please Rolle theorem? I have to prove that the equation $$x^5 +3x- 6$$ can't have more than one real root..so the function is continuous, has a derivative (both in $R$) . In $R$ there must be an interval where $f'(c)=0$, and if I prove this,than the equation has at least one real root. So $5x^4+3 =0$ ..this equation is only true for $x=0$. How to prove that this is the only root?

By Bolzano Theorem since $f(0)=-6$ and $f(2)=32$ we have $f(0)\cdot f(2)<0$ and then f has at least one root in $(0,2)$. 
Moreover, $f'(x)=5x^4+3>0$ so $f$ is strictly increasing and can only have one root.
