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Can x^3-2x^2-2x+m = 0 have three different rational roots?

Source: Vietnam MO 1980 P5

March 17, 2011
algebrapolynomialcalculusintegrationalgebra unsolved

Problem Statement

Can the equation x3−2x2−2x+m=0x^3-2x^2-2x+m = 0 have three different rational roots?
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