RagvaloD wrote: $f(x)$ is square trinomial. Is it always possible to find polynomial $g(x)$ with fourth degree, such that $f(g(x))=0$ has not roots? If $f(x)$ has no real root, any $g(x)$ fits. If $f(x)$ has real root/roots, choose $g(x)=x^4+1+\max(\text{roots of }f(x))$