6

Part of 1997 Federal Competition For Advanced Students, P2

Problems(1)

polynomial (maybe posted before)

Source: Austria 1997

For every natural number

n

, find all polynomials x^2\plus{}ax\plus{}b, where

a^2 \ge 4b

, that divide x^{2n}\plus{}ax^n\plus{}b.

algebrapolynomialalgebra proposed