( a αx + a 2 y + 1 ) 2009 is a polynomial in x and y if the sum of the co-efficients vanishes for some real value of a. Then possible value of α is/are

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x = y = 1 ⇒ ( a α + a 2 + 1 ) 2009 = 0 ⇒ a 2 + a α + 1 = 0 if a is real then b 2 − 4 a c ≥ 0 ⇒ α 2 − 4 ≥ 0 ∴ α = − 2 , − 3 , 2

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