The quintic equation

(1)

is sometimes known as de Moivre's quintic (Spearman and Williams 1994). It has solutions

(2)

for ,
1, 2, 3, 4, where and are given by the simultaneous equations
(Spearman and Williams 1994).
See also
Quintic Equation
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References
Spearman, B. K. and Williams, K. S. "Characterization of Solvable Quintics ."
Amer. Math. Monthly 101, 986992, 1994.Referenced on WolframAlpha
de Moivre's Quintic
Cite this as:
Weisstein, Eric W. "de Moivre's Quintic."
From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/deMoivresQuintic.html
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