  The generic monic polynomial of degree N features N a priori arbitrary
coefficients $c_m$ and N zeros $z_n$. In this paper we limit consideration to
$N = 8$ and $N = 9$. We show that if the $N$ -- a priori arbitrary --
coefficients $c_m$ of these polynomials are appropriately defined -- as it
were, a posteriori -- in terms of 6 arbitrary parameters, then the $N$ roots of
these polynomials can be explicitly computed in terms of radicals of these 6
parameters. We also report the constraints on the N coefficients $c_m$ implied
by the fact that they are so defined in terms of 6 arbitrary parameters; as
well as the explicit determination of these 6 parameters in terms of the N
coefficients $c_m$.
