Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For degree 1, 2, 3 and 4 there is an "extended a,b,c-formula" (like the one we learn in middle or high school, for the solution to a polynomial equation $p(x) = 0$, when the degree is $\geq 5$ there isn't a solution in this form with the help of radicals due to an application of Galois theory.

My question: how far can you get with this kind of (a,b,c)-formulae when you allow non-radical solutions when solving polynomial equations ?

share|cite|improve this question
Are you familiar with solutions obtained using Bring radicals, Jacobi theat functions, and elliptics modular functions? See e.g. Wikipedia, beyond radicals – Bill Dubuque Jan 4 '12 at 22:26
possible duplicate of Finding roots of polynomials with rational coefficients – J. M. Jan 4 '12 at 23:56
In any event: Umemura shows how to use Riemann theta functions to represent roots of arbitrary-order polynomials. See Glasser's preprint as well. – J. M. Jan 5 '12 at 0:02

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.