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Largest roots of cubic polynomials

Problem 356 Published on Saturday, 29th October 2011, 01:00 pm; Solved by 442;
Difficulty rating: 60%

Let an be the largest real root of a polynomial g(x) = x3 - 2n·x2 + n.
For example, a2 = 3.86619826...

Find the last eight digits ofp356_cubicpoly1.gif.

Note: p356_cubicpoly2.gif represents the floor function.