Question

Let a ≠ 0, b and c be real numbers. Show that, if there is areal valued f such that f(f(x)) = ax^2 + bx + c for every real x, then

(b - 1)^2 ≤ 4(ac + 1)

I don't know how to this, but I was told that several guys with a good knowledge in calculus had a lot of trouble and a smart 14- year-old boy gave a correct proof using high school algebra.

Can someone help?

Answer 1

Source?

Answer 2

What do you mean source?

Answer 3

Where is it from?

Answer 4

I saw this question posted on a different platform and nobody solved it. So I was wondering if someone here could.

Answer 5

Where?

Answer 6

This site is hardly full of olympiad-level people FWIW

Answer 7

answers.yahoo.com

Answer 8

Oh lol, probably isn't too hard though then, I thought you meant somewhere like AoPS ¬_¬. Still not my style, though.

Answer 9

What's a AoPS?