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The '''Abel-Ruffini theorem,''' often known just as '''Abel's theorem''', states that it is impossible to solve a general quintic equation "in radicals". This is in stark contrast with [[polynomial|polynomials]] of smaller [[degree]].

The '''Abel-Ruffini theorem,''' often known just as '''Abel's theorem''', states that it is impossible to solve a general quintic equation "in radicals."  This is in stark contrast with [[polynomial|polynomials]] of smaller [[degree]].

Recall that a "quadratic polynomial" is an expression of the form <math>p(x) = ax^2+bx+c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are some real (or complex) coefficients.  It is a familiar fact that the solutions of <math>ax^2+bx+c</math> are given by the [[quadratic formula]] as  

Recall that a "quadratic polynomial" is an expression of the form <math>p(x) = ax^2+bx+c</math>, where <math>a</math>, <math>b</math>, and <math>c</math> are some real (or complex) coefficients.  It is a familiar fact that the solutions of <math>ax^2+bx+c</math> are given by the [[quadratic formula]] as