InterviewSolution
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InterviewSolution
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If the rootsof `10 x^3-n x^2-54 x-27=0`are inharmonic oprogresion, then `n`eqauls_________. |
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Answer» Correct Answer - 9 `10x^(3)-nx^(2)-54x-27`=0 has roots in H.P. put x=1/t `27t^(3)+54t^(2)+nt-10=0` This equation has roots in A.P. Let the roots be a-d,a, and a+d `therefore3a=-(54)/(27)` or `a=-2/3` Also `(a-d)a(a+d)=10/27` `therefore2/3(4/9-d^(2))=-10/27` or `(4/9-d^(2))=-5/9` `therefored^(2)=1` or `d=pm1` So, roots are `1/3,-2/3,-5/3` `thereforen/27=10/9-5/9-2/9` or `n/27=3/9` or n=9 |
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