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?

So you want to prove $5x^4+3=0$ has only one root at $0$? That's not true as $5x^4+3>0$. This establishes the proof
