Editing Nth root (section)

==Solving polynomials==
{{see also|Root-finding algorithms}}

It was once [[conjecture]]d that all [[polynomial equation]]s could be [[Algebraic solution|solved algebraically]] (that is, that all roots of a [[polynomial]] could be expressed in terms of a finite number of radicals and [[elementary arithmetic|elementary operations]]). However, while this is true for third degree polynomials ([[cubic function|cubics]]) and fourth degree polynomials ([[quartic function|quartics]]), the [[Abel–Ruffini theorem]] (1824) shows that this is not true in general when the degree is 5 or greater. For example, the solutions of the equation

<math display="block">x^5 = x + 1</math>

cannot be expressed in terms of radicals. (''cf.'' [[quintic equation]])