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I search all over the Internet for a proof of Descartes's rule of sign. Found a pdf file which has page-long proof that a high schooler has to no way to understand.

Can somebody talented here give me a proof of the rule, in geometry preferably, or if impossible to be done in geometry in simple algebra or trigonometry.

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  • $\begingroup$ There are many theorems whose statements a high schooler can understand, but whose proofs are much more difficult. For example, Fermat's Last Theorem. $\endgroup$ – vadim123 Nov 14 '14 at 0:33
  • $\begingroup$ See also math.stackexchange.com/questions/745583/…. $\endgroup$ – lhf Nov 14 '14 at 1:18

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