A Six Degree Polynomial

The coefficients of a 6th degree polynomial P(x) are integers and its roots are 6 different prime numbers. There exist two integers A and B such that P(A) = 65536 and P(B) = 45441. P(75) < 0. Find the 6 roots. [Explain how you got your answer. -KD]

Source: Reader Philippe Fondanaiche.

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