Three quadratic trinomials all with an integer root
Source: XVII Tuymaada Mathematical Olympiad (2010), Senior Level
August 1, 2011
quadraticscalculusintegrationalgebrapolynomialalgebra unsolvedBaron Munchausen
Problem Statement
Baron Münchausen boasts that he knows a remarkable quadratic triniomial with positive coefficients. The trinomial has an integral root; if all of its coefficients are increased by , the resulting trinomial also has an integral root; and if all of its coefficients are also increased by , the new trinomial, too, has an integral root. Can this be true?