Solving septics in radicals
A novel method to solve certain solvable septic equations is described. The method involves conversion of the given septic to an octic equation by adding a root to it, and then decomposing the octic equation into two fourth-degree polynomial factors. The resulting quartic equations are solved to obtain the roots of the given septic. The condition for the coefficients to satisfy in order that the given septic is solvable in such fashion is derived. The behavior of roots of the septic is discussed.
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