Unitary quadratic trinomials
Source: All-Russian 2007
May 4, 2007
quadraticsalgebra unsolvedalgebra
Problem Statement
Unitary quadratic trinomials and satisfy the following interesting condition: f(g(x)) \equal{} 0 and g(f(x)) \equal{} 0 do not have real roots. Prove that at least one of equations f(f(x)) \equal{} 0 and g(g(x)) \equal{} 0 does not have real roots too.S. Berlov