Holomorphic square root outside all polynomial roots
= Holomorphic square root outside all polynomial roots
An even-degree <polynomial> with all roots in $|z|<R$ admits a <holomorphic square root> throughout $|z|>R$. Factor out its even power of $z$ and use the convergent logarithm of each $1-a_j/z$ to construct it. Even degree removes the annular winding obstruction. The two choices differ by a global sign.