Root Separation for Reducible Monic Quartics

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We study root separation for reducible monic integer polynomials of degree four. If \text{H}(P) is the height and \mathrm{sep}(P) the minimal distance between two distinct roots of a separable integer polynomial P(x) , and \mathrm{sep}(P)=\mathrm{H}(P)^{-e(P)} , we show that \limsup e(P)=2 , where limsup is taken over all reducible monic integer polynomials P(x) of degree 4 .