Abstract.
A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel’s proof, the method produces no solution for the quintic equation.
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Beji, S. A Systematic Approach to the Exact Roots of Polynomials. MedJM 5, 163–172 (2008). https://doi.org/10.1007/s00009-008-0141-6
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DOI: https://doi.org/10.1007/s00009-008-0141-6