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in Olympiad by (76.5k points)

Let P(x) = x2 + ax + b be a quadratic polynomial with real coefficients. Suppose there are real numbers s ≠ t such that P(s) = t and P(t) = s. Prove that b - st is a root of the equation x2 + ax + b – st = 0.

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s2 + as + b = t        ..(1)

t2 + at + b = s         ..(2)

Add (1) & (2)

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