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# polynomial

This is a discussion on polynomial within the Pre-Algebra and Algebra forums, part of the Pre-University Math category; A polynomial $f(x)$ has Integer Coefficients such that $f(0)$ and $f(1)$ are both odd numbers. prove that $f(x) = 0$ ...

1. A polynomial $f(x)$ has Integer Coefficients such that $f(0)$ and $f(1)$ are both odd numbers. prove that $f(x) = 0$ has no Integer solution

2. Originally Posted by jacks
A polynomial $f(x)$ has Integer Coefficients such that $f(0)$ and $f(1)$ are both odd numbers. prove that $f(x) = 0$ has no Integer solution
There are details you may need to fill in yourself but:

$$f(0)$$ odd implies that the constant term is odd

then $$f(1)$$ odd implies that there are an even number of odd coeficients of the non constant terms.

So if $$x \in \mathbb{Z}$$ then $$f(x)$$ is odd and so cannot be a root of $$f(x)$$

CB

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