Saturday, May 5, 2018

polynomials - A contest math problem


Let P(x) be a polynomial with integer coefficients of degree d>0.




  1. If α and β are two integers such that P(α)=1 and P(β)=1, then prove that |βα| divides 2.


  2. Prove that the number of distinct integer roots of (P(x))21 is at most d+2.




First one is very easy. But I cannot understand how to prove the second one. I would appreciate any help.

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