$f(x),g(x),h(x)$ 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.
Source: St Petersburg Olympiad 2009, Grade 10, P3
Tags: algebra
$f(x),g(x),h(x)$ 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.