let P_n an n-polynomial. let a_1 ,...,a_n its simple roots let m_k the slope of the tangent to P_n at the point (a_k ,0) prove that Σ_(k=1) ^n (1/m


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Question Number 104775 by MAB last updated on 23/Jul/20

$l e t P_{n} a n n - p o l y n o m i a l .$ $l e t a_{1}, . . ., a_{n} i t s s i m p l e r o o t s$ $l e t m_{k} t h e s l o p e o f t h e t a n g e n t t o P_{n} a t$ $t h e p o i n t (a_{k}, 0)$ $p r o v e t h a t$ $\underset{k = 1}{\sum^{n}} \frac{1}{m_{k}} = 0$ $w h a t a b o u t m u l t i p l e r o o t s ?$
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