Mike

Hi, my name's Mike.
I'm doing a report on finding zeroes/roots of polynomials. I'm very interested in what they call Cardano's method/theorem for fining cubic roots. Although his name comes up several times all over the web nobody ever cites the actual formula. I was wondering if you knew what it was and could send/tell me it? Also, is there a formula for quartic equations? Anything u could give me will be gratefully accepted,
thanx Mike.

Hi Mike.
Cardan's method is a way to express the roots of the cubic polynomial p(x) = x^3 + a x^2 + b x + c as a combination of square roots, cube roots and rational functions of a, b and c. Also finding the roots of a fourth degree polynomial can be reduced to the problem of solving a certain cubic. These expression are of theoretical interest since they contrast the case of polynomials of fifth degree and higher, where no such universal method can be given, but they are of almost no practical interest.

Rather than try to write these expressions I will give you two references.

Heinrich Tietze, Famous Problems of Mathematics, Graylock Press, New York 1965.
(chapter 10 page 211)

I.N. Herstein, Topics in Algebra, Blaisdell Pub. Co, New York, 1964.
(page 209)

Harley

Go to Math Central

To return to the previous page use your browser's back button.