If a reduced quartic equation x^4 + ax^2 + bx + c = 0 has two positive and two negative roots, there is a simple procedure for generating 24 points in the Cartesian plane, the positions of which depend solely on the roots. These points are not randomly scattered but are arranged in 6 equal circles with a radius R that depends exclusively on the coefficients a, b, c. Behind this unexpectedly complex and organized structure lie geometric methods for solving the quartic equation that had remained unknown until now.
georgeplousos George Plousos
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The unknown geometry of the roots of the quartic equation

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