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-k-1-n-1-x-k-a-interms-of-p-p-and-a-2-calculste-S-2-k-1-n-1-x-k-a-2-interms-of-p-p-

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 .