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in Olympiad by (76.3k points)

Let P(x) = x2 + ax + b be a quadratic polynomial where a is real and b ≠ 2 is rational. Suppose P(0)2 , P(1)2, P(2)2 are integers. Prove that a and b are integers.

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As b is rational number and (P(0))^2 is integer hence b will be an integer

Hence a is an integer

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