a question a day keeps the stupid away 26
Abel’s impossibility theorem states that there is no general algebraic solution (that is, a solution using the algebraic functions, which are addition, multiplication, and taking n-th roots) to polynomials of degree five or higher.
Which isn’t to say that every polynomial of degree five or higher can’t be solved algebraically. For example, the 16th degree polynomial 0 = (x - 2)^16 can be solved trivially using the algebraic functions.
Solve the general polynomial of arbitrary degree using the non-algebraic (in other words, transcendental) functions, as well as the algebraic functions as necessary.