Analytical formula for the roots of the general complex cubic polynomial

Ibrahim Baydoun (1)

1 IL - Institut Langevin - Ondes et Images (UMR7587)

We present a new method to calculate analytically the roots of the general complex polynomial of degree three. This method is based on the approach of appropriated changes of variable involving an arbitrary parameter. The advantage of this method is to calculate the roots of the cubic polynomial as uniform formula using the standard convention of the square and cubic roots. In contrast, the reference methods for this problem, as Cardan-Tartaglia and Lagrange, give the roots of the cubic polynomial as expressions with case distinctions which are incorrect using the standar convention.

Mots clés: cubic polynomial roots; analytical uniform formula; appropriated change of variable

Domaines: Algèbre commutative [math.AC]

Ibrahim Baydoun. Analytical formula for the roots of the general complex cubic polynomial. 2018. ⟨hal-01237234v2⟩