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Tuymaada 2010, Junior League, Problem 3

Source:

July 18, 2010
quadraticsalgebrapolynomialVietaabsolute valuealgebra unsolved

Problem Statement

Let f(x)=ax2+bx+cf(x) = ax^2+bx+c be a quadratic trinomial with aa,bb,cc reals such that any quadratic trinomial obtained by a permutation of ff's coefficients has an integer root (including ff itself). Show that f(1)=0f(1)=0.
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