Thread: Solvable Quintics

Hey

As I understand it, linear, quadratic, cubic and quartic equations can all be solved through the factorization into radicals, or parts per x, however it is apparent that there are some quintics that can and can't be solved.

What radicals in a general quintic determine whether or not it can be solved?

And if there are some that can be solved, is it possible that its anti-derivative cannot be solved either? Does it even have an an anti-derivative?

Thanks for any solutions in advance.

All polynomials can be solved in the sense that every polynomial of degree n has n roots (possibly with multiples). Quintics just don't have any explicit, general formula for finding those roots.

Also, all polynomials can be easily differentiated and integrated regardless of what you know about their roots.