  Let $\mu$ be a compactly supported probability measure on the real line.
Bercovici-Voiculescu and Nica-Speicher proved the existence of a free
convolution power $\mu^{\boxplus k}$ for any real $k \geq 1$. The purpose of
this short note is to give an elementary description of $\mu^{\boxplus k}$ in
terms of of polynomials and roots of their derivatives. This bridge allows us
to switch back and forth between free probability and the asymptotic behavior
of polynomials.
