Bring radical

The Bring radical, also called the ultraradical, is a function that gives the unique real root of the polynomial equation x^5 + x + a, defining x as an algebraic function of a. It is the simplest algebraic function that cannot be expressed using ordinary radicals, meaning root-extraction operations alone. It is named after the Swedish mathematician Erland Bring, who introduced it in the eighteenth century; later, George Jerrard showed that certain quintic equations can be solved using ordinary radicals together with the Bring radical, by transforming a general quintic into a simplified normal form. Because the Abel-Ruffini theorem rules out a general radical solution for quintic equations, the Bring radical supplies the extra tool needed to give quintics a closed form solution, in the same way that other special functions provide closed forms for equations that ordinary radicals alone cannot solve.