KöMaL 2007 A430

Let $n \ge$2 and let $u_1=1,u_2,\ldots,u_n$ be arbitrary complex numbers with absolute values at most 1 and let $f$($x$)=($x$-$u_1$)($x$-$u_2$)...($x$-$u_n$). Prove that polynomial $f$'($x$) has a root with a non-negative real part.