Let $Q(z)=(z-{\alpha}_{1})\cdots (z-{\alpha}_{n})$ be a polynomial of degree $>1$ with distinct roots outside the real line.

We have

$\sum _{j=1}^{n}\frac{1}{{Q}^{\prime}({\alpha}_{j})}=0.$

Do we have a proof relying on rudimentary techniques?

We have

$\sum _{j=1}^{n}\frac{1}{{Q}^{\prime}({\alpha}_{j})}=0.$

Do we have a proof relying on rudimentary techniques?