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x^3 - 3cx^2 - dx + c = 0 has no more than one rational root.

Source: Polish MO Recond Round 1982 p1

September 9, 2024
algebrapolynomial

Problem Statement

Prove that if c,d c, d are integers with c≠d c \neq d , d>0 d > 0 then the equation x3−3cx2−dx+c=0 x^3 - 3cx^2 - dx + c = 0 has no more than one rational root.
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