is there any short method to determine that how many real roots a cubic equation has

Question

directrix · Answer

Descartes' Rule of Signs will help determine the number of real roots which you can expect but the results are not definitive. By that, I mean you might get that the roots could be 2+ real roots and 1 - real root, or other assortments of possibilities.

directrix · Answer

Do you have a particular cubic equation in mind?

sid123 · Answer

yes that is (x-a)^3 +(x-b)^3 +(x-c)^3 where a b c are distinct real and i have to get distinct roots

directrix · Answer

This problem may be beyond any help from Descartes. Look at what WolframAlpha did with it before running out of time: http://www.wolframalpha.com/input/?i=+%28x-a%29%5E3+%2B%28x-b%29%5E3+%2B%28x-c%29%5E3%3D0

sid123 · Answer

thanks

directrix · Answer

What math course are you taking in which this problem was assigned? There should be somebody here who knows how to do it.

sid123 · Answer

it is in an exam paper csir net