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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proof for quadratics

| Comment 6 of 7 |

I can prove the quadratic case with odd coefficients.

Odd squares = 1 mod8.

Discriminant D = b^2-4ac = 1-4 = -3 = 5 mod8, so D is not a square and the equation has no rational roots.

Posted by xdog on 2023-10-30 19:16:18

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