We know that fifth (or higher) degree polynomial equation has no general solution formula using only the usual algebraic operations (addition, subtraction, multiplication, division) and application of radicals (square roots, cube roots). (Not solvable using radicals).

But can those polynomial equation have general "closed" formula solution if we allow more operations (and functions) in solution, such as: log functions, exponential functions, trigonometric functions, or other type of functions, etc.

Does such "closed" formula solution exist ?

  • $\begingroup$ The quintic can be solved with elliptic functions of the coefficients, in addition to the other you mentioned. $\endgroup$ – egreg Sep 12 '14 at 16:34
  • $\begingroup$ Possible duplicate of this. $\endgroup$ – Lucian Sep 12 '14 at 19:32

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