Explicitly solvable algebraic equations of degree 8 and 9
Abstract
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 $c_m$.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.12057
 Bibcode:
 2021arXiv211112057C
 Keywords:

 Mathematics  Dynamical Systems
 EPrint:
 5 pages