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If a polynomial has only integer roots, is it always possible to find a root using the rational roots theorem?

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    Yes. That's what the rational root theorem guarantees (given that you can factor the constant term).2011-12-19
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    It's difficult to answer till you clarify precisely what you mean by "find a root". E.g. it could mean anything ranging from a nonconstructive existence proof to a polynomial time root-finding algorithm.2011-12-20

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