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?
TUYMAADA 2010
Tuymaada Olympiad 2010.