P is apolynomial from C_n [x] having n roots (x_i )_(1≤i≤n ) and x_i # x_j for i#j 1) prove that Σ_(i=1) ^n (1/(p^′ (x_i ))) =0 2) find Σ_(i=1) ^n (x_i ^k /(p^′ (x


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Question Number 28368 by abdo imad last updated on 24/Jan/18

$P i s a p o l y n o m i a l f r o m C_{n} [x] h a v i n g n r o o t s$ $You can't use 'macro parameter character #' in math mode$ $1) p r o v e t h a t \sum_{i = 1}^{n} \frac{1}{p^{^{'}} (x_{i})} = 0$ $2) f i n d \sum_{i = 1}^{n} \frac{x_{i}^{k}}{p^{^{'}} (x_{i})} w i t h k \in [[0, n - 1]] .$
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