Solving cubic equations
Solving cubic equations
Just as the Greeks had done before, the Italian mathematicians also divided equations according to types, tolerating only positive members. (This had its origin in the Greeks' tendency to interpret quantities geometrically, which excluded negative values). For example, the quadratic equations
x^2+px=q and x^2+q=px
were distinguished and solved in different ways. This was also done with cubic equations - homework help at domyhomeworkclub , and it was suspected (rightly, as it turned out later) that Del Ferro had successfully worked on the type and passed on the solution procedure to Fiore.
With unspeakable efforts and nights of work, Tartaglia managed not only to rediscover this path, but also to solve the type x^3+ax=b. Moreover, with the skilful substitution z=x-a/3, he succeeded in eliminating the quadratic member from the general form of the cubic equation z^3+az^2+bz+c=0. This made almost all cubic equations solvable, and a solution formula emerged.
After his victory in the aforementioned competition - matlab homework help , Tartaglia was pressured into revealing his method, the knowledge of which, however, promised him advantages as long as it remained his sole possession. It was not until 1539 that the mathematician Geronimo Cardano succeeded in eliciting the formula from him.
Although Cardano had previously sworn not to pass on the solution formula - excel homework help , he later published it in his "Ars magna". Although he acknowledged the achievements of Tartaglia and Del Ferro, a bitter dispute broke out between Tartaglia and Cardano , and in the end the formula went down in mathematics as the Cardanian formula.
Tartaglia continued to achieve remarkable things in the following years, but he was embittered.
He died in Venice on 14 December 1557.
More information:
Peter Josephus Wilhelmus Debye
Types of programming languages
Polynomials, coefficient relationships
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