TOPICS
Search

de Moivre's Quintic

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

The quintic equation

x^5+ax^3+1/5a^2x+b=0
(1)

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

x_j=omega^ju_1+omega^(4j)u_2
(2)

for j=0, 1, 2, 3, 4, where omega=e^(2pii/5) u_1 and u_2 are given by the simultaneous equations

u_1^5+u_2^5=-b
(3)
u_1^5u_2^5=-(1/5a)^5
(4)

(Spearman and Williams 1994).

See also

Quintic Equation

Explore with Wolfram|Alpha

References

Spearman, B. K. and Williams, K. S. "Characterization of Solvable Quintics x^5+ax+b." Amer. Math. Monthly 101, 986-992, 1994.

Referenced on Wolfram|Alpha

de Moivre's Quintic

Cite this as:

Weisstein, Eric W. "de Moivre's Quintic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deMoivresQuintic.html

Subject classifications