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?

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