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$N$ is the number of positive roots of $$P(x)=\sum_{k=0}^n a_k x^k$$

$M$ is the number sign change in the sequence of non-zero coefficients. Prove that $M \geq N$ and $2 \mid (M-N)$.

It's quite common but I still can't have any idea. Please help me :((

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    C'mon, Descartes proved this centuries ago, so you should be able to do it too! – 2017-01-08

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