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the coefficient of x 49 in the polynomial {x-(C 1/C0 )}{x-2 2 (C 2/C1 )}{x-3 2 (C 3/C2 )}.....{x-50 2 (C 50/C49 ) is........? ans in the form of summation will do and give the steps followed.

the coefficient of x49 in the polynomial {x-(C1/C0)}{x-22(C2/C1)}{x-32(C3/C2)}.....{x-502(C50/C49) is........?


ans in the form of summation will do and give the steps followed.

Grade:Upto college level

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear nishant

let the polinomial is

 x50 + A49x49 +A48 x48...........+ A1 x +A0 =0

 whose roots are  (C1/C0) ,22(C2/C1) ,32(C3/C2) ......502(C50/C49)

so   sum of roots = -A49

      A49 =  -[ (C1/C0) + 22(C2/C1)+  32(C3/C2) ......+502(C50/C49)]

             =     r :1 to 50  ∑-r2(Cr/C r-1)

             =     r :1 to 50  ∑r2-51r

             =   r :1 to 50  ∑r2     -   r :1 to 50   ∑51r

             =  22100

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