Given odd positive integer $n$ and a monic polynomial $f(x)=(x-x\_1)\dots (x-x\_n)$ with $n$ distinct real roots. Is it always true that $\sum f'(x\_i) > 0$? I may prove it for $n=3$ and $n=5$ and it looks plausible.



sum of derivatives in roots of a polynomial of odd degree
If I'm not mistaken this is basically the same question as [this](http://www.artofproblemsolving.com/Forum/viewtopic.php?p=366673&sid=0f77743cc628257f609bb649b7ecfc84#p366673) question from the international mathematical olympiad in 1971. The statement is only true for 3 and 5 variables showing that there is no obvious generalization to [Schur's inequality](http://en.wikipedia.org/wiki/Schur%27s_inequality) in many variables.


