MathDB

Indonesia National Science Olympiad 2010 - Day 2 Problem 7

Source:

September 28, 2010

algebrapolynomialalgebra unsolved

Problem Statement

Given 2 positive reals

a

and

b

. There exists 2 polynomials

F(x)=x^2+ax+b

and

G(x)=x^2+bx+a

such that all roots of polynomials

F(G(x))

and

G(F(x))

are real. Show that

a

and

b

are more than

6

.
Raja Oktovin, Pekanbaru