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Cubic Equations from an Analytic Point of View

Abstract–About five hundred years ago, the first algebraic solution of a class of cubic equations was discovered by Scipione del Ferro. In The Great Art (1545), Girolamo Cardano devoted 13 chapters to an attempt to solve all cubics, which was unsuccessful in precisely those cases in which the cubic possessed three (real) solutions. About 50 years later, François Viète discovered a trigonometric method for dealing with the cases that had eluded Cardano. It turns out that the method of Viète can be used to solve all cases and provide analytic insight into Cardano’s bewilderment.