Cubic equation

In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third power. An example is the equation

History

The Iranian mathematician Omar Khayyám (1048–1123) constructed solutions of cubic equations by intersecting a conic section with a circle. He showed how this geometric solution could be used to get a numerical answer by consulting trigonometric tables.

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In the early sixteenth century, the Italian mathematician Scipione dal Ferro found a method for solving a class of cubic equations, namely those x3 + mx = n. In fact, all cubic equations can be reduced to this form if we allow m and n to be negative, but negative numbers were not known at that time. Dal Ferro kept his achievement secret until just before his death, when he told his student about it. Tartaglia heard about this and soon found a method himself. He revealed his method to Gerolamo Cardano, who published it in Ars Magna 1545.

Related Topics:
Scipione dal Ferro - Tartaglia - Gerolamo Cardano - 1545

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Cardano noticed that Tartaglia's method sometimes required him to extract the square root of a negative number. He even included a calculation with these complex numbers in Ars Magna, but he did not really understand it. Rafael Bombelli studied this issue in detail and is therefore often considered as the discoverer of complex numbers.

Related Topics:
Complex number - Rafael Bombelli

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