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x^2-2x[x]+x-alpha=0

Source:

October 16, 2010
algebrapolynomialsum of rootsfloor function

Problem Statement

Find all numbers α\alpha for which the equation x2−2x[x]+x−α=0x^2 - 2x[x] + x -\alpha = 0 has two nonnegative roots. ([x][x] denotes the largest integer less than or equal to x.)
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