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Find the co-efficient of x^99 in the following expression: (x-1)(x-2)(x-3).....(x-100) please give the solution

Find the co-efficient of x^99 in the following expression:
(x-1)(x-2)(x-3).....(x-100)
please give the solution

Grade:11

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago

Say the function if f(x) = (x-1)(x-2)...(x-100)
The roots of this function is 1, 2, 3,... 100
f(x) = x^100 + ax^99 + bx^98 .... + n
sum of roots = -a = 1 + 2 .. 100 = 100(101)/2 = 5050
Hence, coeff of x^99 = -5050
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty

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