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in Olympiad by (76.3k points)

Let P(x) = x2 + ax + b be a quadratic polynomial where a and b are real numbers. Suppose [P(–1)2, P(0)2, P(1)2] is an arithmetic progression of integers. Prove that a and b are integers.

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So if b is any rational number then it can be integer only as its square is integer.

should be rational which is not possible for any integer value of m

=> b can not be irrational.

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