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On a recent test in a course I'm TAing, students were asked to prove that sin(x) is not a rational function by using the fact that polynomials only have finitely many zeroes. During my tutorial, I'd like to show them some other interesting problem whose (reasonably short!) solution uses the fact that polynomials only have finitely many zeroes. What's your favourite?

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    I should specify that the students are first year students, but it's a fairly advanced course, so they are generally bright but don't know much college math other than calculus and linear algebra.2012-02-15

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