InterviewSolution
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InterviewSolution
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Let nge3 be an integer. For a permutaion sigma=(a_(1),a_(2),.....,a_(n)) of (1,2,.....,n) we let f_(sigma)(x)=a_(n)X^(n-1)+a_(n-1)X^(x-2)+....+a_(2)x+a_(1). Let S_(sigma) be the sum of the roots of f_(sigma)(x)=0 and let S denote the sum over all permutations sigma of (1,2,.....,n) of the numbers S_(sigma). Then- |
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Answer» `Slt0n!` `AAlambda=a_(1)+a_(2)+....+a_(n)` `S=-[(a_(1)+a_(2)+....+a_(n))((1)/(a_(1))+(1)/(a_(2))+.....+(1)/(a_(n)))-n]` `S=n-(a_(1)+a_(2)+....+a_(n))((1)/(a_(1))+(1)/(a_(2))+.....+(1)/(a_(n)))` FOM `A.M.geH.M` `(a_(1)+a_(2)+....+a_(n))((1)/(a_(1))+(1)/(a_(2))+.....+(1)/(a_(n)))GEN^(2)` `Sle-n(n-1)` |
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