let p∈C[x] degp=n (x_i )_(1≤k≤n) the roots of p(x) a∈C?/p(a)≠0 1) calculate S_1 = Σ_(k=1) ^n (1/(x_k −a)) interms of p,p^′ and a 2)calculste S_2 =Σ_(k=1) ^n (1/((x_k −a)^2 )) interms of p,p^, p^(′′) and a.


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Question Number 34607 by abdo mathsup 649 cc last updated on 08/May/18

$l e t p \in C [x] d e g p = n {(x_{i})}_{1 ⩽ k ⩽ n} t h e r o o t s o f p (x)$ $a \in C ? / p (a) \neq 0$ $1) c a l c u l a t e S_{1} = \sum_{k = 1}^{n} \frac{1}{x_{k} - a} i n t e r m s o f p, p^{^{'}} a n d a$ $2) c a l c u l s t e S_{2} = \sum_{k = 1}^{n} \frac{1}{{(x_{k} - a)}^{2}} i n t e r m s o f p, p^{,}$ $p^{^{″}} a n d a .$
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