Problem

Source: Russian TST 2016, Day 8 P1 (Group NG), P2 (Groups A & B)

Tags: algebra, polynomial, Inequality



For which even natural numbers $d{}$ does there exists a constant $\lambda>0$ such that any reduced polynomial $f(x)$ of degree $d{}$ with integer coefficients that does not have real roots satisfies the inequality $f(x) > \lambda$ for all real numbers?