We all know the solution of ax2+bx+c=0. There is an analogous formula for polynomials of degree three. See https://math.vanderbilt.edu/schectex/courses/cubic/

Thank you Prof. Ada, I already know the method of Cardano for solveing the equation of the third degree. I am asking about a new treatment to solve the third degree equation by using the method used to solve the fourth degree equation

If we multiply a cubic equation x3+ax2+bx +c = 0 with (x-α), where α is a (suitable) real number, then we obtain the algebraic equation of degree 4, whose solutions can be obtained using routine calculations applying Ferrari’s method. Namely, one of these four solution is α, while other three solutions are in fact the solutions of given equation x3+ax2+bx +c = 0.

Thank you very much Prof. Romeo. In fact, when I was a student, I used to solve many polynomial equations of degree 3 by using Ferrari's method.

Dear Maged Z. Youssef ,

The attached papers include an interesting unified approach to solve and find polynomial roots using matrix techniques.

(1) D.Kalman and J.E. White,Polynomial equations and circulant matrices

, The American Mathematical Monthly, 108 ( 2001) 821-840.

(2) On a class of matrices generated by certain generalized permutation matrices and applications

Best regards