Roots of a cubic polynomial

Roots of a cubic polynomial is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Find all eigenvalues of a real 3x3 matrix and estimate their errors.

See Wikipedia Cubic equation. Example. [1]

a*x**3 + b*x**2 + c*x + d = 0

matrix: [[1,-10], [0,1,-1],[0,0,1]]

polynomial: [a,b,c,d] =[1, -3,+3, -1]

roots: [1,1,1]