Loterre: Mathematics: Bring radical

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algebra > polynomial > polynomial equation > Bring radical

mathematical analysis > equation > polynomial equation > Bring radical

Bring radical

In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial
${\\displaystyle x^{5}+x+a\\,}$

The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen such that the Bring radical is real-valued for real a and is an analytic function in a neighborhood of the real line. Because of the existence of four branch points, the Bring radical cannot be defined as a function that is continuous over the whole complex plane, and its domain of continuity must exclude four branch cuts.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Bring_radical)

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