trinomial P_1 + P_2 + P_3 has real roots if every 2 have common root
Source: 2011 Brazil IMO TST 2.1
July 24, 2021
trinomialpolynomialalgebra
Problem Statement
Let , and be polynomials of degree two with positive coefficient leader and real roots . Prove that if each pair of polynomials has a common root , then the polynomial has also real roots.