• Corpus ID: 233168608

Two classes of explicitly solvable sextic equations

@inproceedings{Calogero2021TwoCO,
  title={Two classes of explicitly solvable sextic equations},
  author={Francesco Calogero and F. Payandeh},
  year={2021}
}
The generic monic polynomial of sixth degree features 6 a priori arbitrary coefficients. We show that if these 6 coefficients are appropriately defined—in two different ways—in terms of 5 arbitrary parameters, then the 6 roots of the corresponding polynomial can be explicitly computed in terms of radicals of these parameters. We also report the 2 constraints on the 6 coefficients of the polynomial implied by the fact that they are so defined in terms of 5 arbitrary parameters; as well as the… 
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References

General Formulas for Solving Solvable Sextic Equations

Abstract Let G be a transitive, solvable subgroup of S6. We show that there is a common formula for finding the roots of all irreducible sextic polynomials f(x) ∈ Q[x] with Gal(f) = G. Moreover, once…