perplexus.info :: Just Math : Even degree and Odd coefficient Crossed Polynomial Poser

Even degree and Odd coefficient Crossed Polynomial Poser (Posted on 2023-10-29)

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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Request for Clarification

| Comment 1 of 7

Does "odd number" in the problem statement imply that the coefficients must also be positive?

Otherwise, P(x) = x^2 - 1 seems to fit the bill, but that doesn't feel like a D3 problem...

Posted by H M on 2023-10-29 07:21:29

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