1990 OIM Problems/Problem 6

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Problem

Let $f(x)$ be a polynomial of degree 3 with rational coefficients. Prove that if the graph of $f$ is tangent to the x-axis, then $f(x)$ has its 3 rational roots.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

https://www.oma.org.ar/enunciados/ibe5.htm