Polynomial root separation examples

In vol. 32 of this Journal, G.E. Collins reported on extensive calculations supporting his conjecture that the exponent in the well-known Mahler–Mignotte bound for the root separation of squarefree integral polynomials of degree n might be replaceable with −n/2. This paper exhibits infinite sequences of cubic polynomials with ‘true’ exponent −2, thus disproving that conjecture for degree n=3, and extends this to analogous bounds for close root triplets of quartic polynomials.