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Mathematics
General Math
Prove an nth-degree polynomial has exactly n roots
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[QUOTE="Happiness, post: 5485651, member: 549579"] Oh, this is a good point! Then I've not established that ##f(x)## can be written in the form (1.8) with ##A## being a constant, but only that ##f(x)=g(x)(x-\alpha_1)(x-\alpha_2)...(x-\alpha_r)## where ##g(x)## is a polynomial. Wikipedia: "In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept." [URL]https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra[/URL] Does it mean there is no elementary proof for this theorem? [/QUOTE]
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Forums
Mathematics
General Math
Prove an nth-degree polynomial has exactly n roots
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