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-A. `Slt0n!`B. `-n!ltSlt0`C. `0lt Slt n!`D. `n!leS` |
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Answer» Correct Answer - B `S=-[(lambda-a_(n))/(a_(jn))+(lambda-a_(n-1))/(a_(n-1))+.....+(lambda-a_(1))/(a_(1))]` `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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