Expert: Paul Klarreich - 3/24/2006

Question
Hello. There are algorhythms for sloving quadratic, cubic and quartic equations. Is there an algabraic algorithm for solving quintic equations? Please let me know. Thank you.  
Sincererly,
Jason Goldman
JGoldman10@yahoo.com

Answer
Hi, Jason,

You wrote:

Subject:  Solving the Quintic
Question:  Hello. There are algorhythms for sloving quadratic, cubic and quartic equations. Is there an algabraic algorithm for solving quintic equations? Please let me know. Thank you.
Sincererly,
Jason Goldman
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No.

And, by the way, the algorhythms were a doo-wop group of the 70's -- methods for solving problems are algorithms.

Well, the long answer is:
There are formulas for cubics and quartics named for some obscure Italian mathematicians but nobody will ever find a formula for any equation of higher degree.

There is a subject in algebra known as Galois Field Theory which contains the proof that while equations of degree <= 4 are solvable in radicals (i.e. there is a formula) all equations of degree > 4 are not.