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a, b,c rational roots of x^3+ax^2 + bx + c = 0

Source: Singapore Open Math Olympiad 1995 2nd Round p1 SMO

April 2, 2020
polynomialrationalalgebraroots

Problem Statement

Suppose that the rational numbers a,ba, b and cc are the roots of the equation x3+ax2+bx+c=0x^3+ax^2 + bx + c = 0. Find all such rational numbers a,ba, b and cc. Justify your answer
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