## Largest roots of cubic polynomials

### Problem 356

Published on Saturday, 29th October 2011, 01:00 pm; Solved by 349; Difficulty rating: 60%
Let `a`_{n} be the largest real root of a polynomial `g`(x) = x^{3} - 2^{n}·x^{2} + `n`.

For example, `a`_{2} = 3.86619826...

Find the last eight digits of.

__ Note__: represents the floor function.