Gerolamo Cardano is credited with publishing the first formula for solving cubic equations, attributing it to Scipione del Ferro.Gerolamo Cardano
How was the cubic formula derived?
for real numbers a, b, c, d with a≠0. By the fundamental theorem of algebra this equation has three roots x1, x2, x3, over the complex numbers. Using the factor theorem gives the factorization ax3+bx2+cx+d=a(x−x1)(x−x2)(x−x3).
Who solved the cubic?
The solution to the cubic (as well as the quartic) was published by Gerolamo Cardano (1501-1576) in his treatise Ars Magna. However, Cardano was not the original discoverer of either of these results. The hint for the cubic had been provided by Niccolò Tartaglia, while the quartic had been solved by Ludovico Ferrari.
Why is there no quintic formula?
Any cubic formula built solely out of field operations, continuous functions, and radicals must contain nested radicals. There does not exist any quintic formula built out of a finite combination of field operations, continuous functions, and radicals.