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Even degree and Odd coefficient Crossed Polynomial Poser (Posted on 2023-10-29) Difficulty: 3 of 5
P(x) is a polynomial of even degree. Also, all the coefficients of P(x) are odd numbers.

Is it possible for P(x) to have a rational root?
• If so, provide an example.
• If not, prove that it is NOT possible for P(x) to have a rational root.

No Solution Yet Submitted by K Sengupta    
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re: Request for Clarification | Comment 2 of 7 |
(In reply to Request for Clarification by H M)

From how I read the problem, x^2-1 is not a valid polynomial: the coefficient of the linear term is 0, which is even.


If our polynomial is a_(2k)*x^(2k) + a_(2k-1)*x^(2k-1) + ... + a_1*x + a_0, then all the coefficients {a_2k, a_2k-1, ..., a_1, a_0} are odd integers.

(Apologies for lack of proper subscripts and superscripts)

  Posted by Brian Smith on 2023-10-29 09:43:02
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