Editing Abel–Ruffini theorem (section)

==Cayley's resolvent==
Testing whether a specific quintic is solvable in radicals can be done by using [[Quintic function#Cayley's resolvent|Cayley's resolvent]]. This is a [[Polynomial|univariate polynomial]] of degree six whose coefficients are polynomials in the coefficients of a generic quintic. A specific [[irreducible polynomial|irreducible]] quintic is solvable in radicals if and only, when its coefficients are substituted in Cayley's resolvent, the resulting sextic polynomial has a [[rational number|rational]] root, which can be easily tested for using the [[rational root theorem]].