Two classes of explicitly solvable sextic equations

  • Francesco Calogero Physics Department, University of Rome ”La Sapienza”, Rome, Italy
  • Farrin Payandeh Department of Physics, Payame Noor University, PO BOX 19395-3697 Tehran, Iran


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 explicit determination of these 5 parameters in terms of the 6 coefficients of the sextic polynomial.