RU-SPB 2009 Problem 103

$f(x),g(x),h(x)$ are square trinomials with discriminant, that equals $2$ . And $f(x)+g(x),f(x)+h(x),g(x)+h(x)$ are square trinomials with discriminant, that equals $1$ . Prove,that $f(x)+g(x)+h(x)$ has not roots.