I seem to recall from my undergrad days that a cubic polynomial could be readily factored (even analytically) if you appy the assumption that you will have 1 REAL root & the other 2 are complex conjugate pairs. I cannot seem to find my old lecture notes & see nothing on the web on this matter.
Anyone here have any knowledge on this subject? I have played with MATLAB & altered the polynomial coefficients such that whenever complex roots do crop up they are indeed complex conjugate pairs with the 3rd root being REAL.
I would like to treat the 3rd order polynomial generically such that I can evaluate the roots symbolically for the following:
x^3=A*x^2+B*x+C=0 I should be able to factor it so that:
(x+a)(x+b)(x+c)=0 where the a root is REAL & b & c are complex conjugates of each other & express them in terms of the coefficients A, B, & C, but I am striking out with MAPLE.