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About the graph of a polynomial

Source: Iberoamerican Olympiad 1990, Problem 6

May 18, 2007
algebrapolynomialalgebra proposed

Problem Statement

Let f(x)f(x) be a cubic polynomial with rational coefficients. If the graph of f(x)f(x) is tangent to the xx axis, prove that the roots of f(x)f(x) are all rational.
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