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Smaller root of a difference of products of polynomials with integer bounded coefficients

Is there a positive constant $K>0$ such that for every polynomials $f_1,\dots,f_4 \in\mathbb{Z}[X]$ with coefficients in {-1,0,1}, every positive root $x$ of the polynomial $$g=f_1f_2-f_3f_4$$ ...
A. Lampadophore's user avatar