Polynomial root finding algorithm

(*start*)
(*Mathematica 8*)
Clear[x, polynomial, X, y, polynomialdegree];
polynomialdegree = 5;
ycoefficient = -Rationalize[RandomComplex[{-1 - I, 1 + I}],
   0]; polynomial =
 Sum[Rationalize[RandomComplex[{-1 - I, 1 + I}], 0]*x^n, {n, 0,
    polynomialdegree - 1}] +
  If[ycoefficient == 0, -1, ycoefficient]*y^polynomialdegree;
Print["The polynomial is: ", polynomial];
nn = 8000;
Do[Clear[x, X, y];
 X = y /. Solve[polynomial == 0, y, WorkingPrecision -> 100][[i]];
 x = 0;
 Table[x = N[Round[X, 10^-30], 30], {n, 1, nn}];
 y = x;
 Print["x", i, " = ", x, " polynomial value at x", i, " is: ",
  polynomial];, {i, 1, polynomialdegree}]
(*end*)