TITLE: Why can't there be a quintic formula?
QUESTION [9 upvotes]: Possible Duplicate:
Why is it so hard to find the roots of polynomial equations? 

For polynomials (with real coefficients), in degrees 2, 3, 4, there are the quadratic, cubic, and quartic formula, though the quartic formula is extremely long, so what makes degree 5 special that makes writing down a formula impossible?

REPLY [5 votes]: There certainly can be (and is) a formula.  It's just not a formula with radicals.  Others have mentioned why you can't do it with radicals, having to do with the solvable symmetries, but don't confuse this as to there being no formula at all.  A good start might be to investigate Bring Radicals.