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The coefficient of x99 in the polynomial (x – 1) (x – 2) . . . . . . . . (x – 100) is . . . . . . . . . . . . . . . .

The coefficient of x99 in the polynomial (x – 1) (x – 2) . . . . . . . . (x – 100) is . . . . . . . . . . . . . . . .

Grade:11

3 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
Given polynomial:
(x – 1) (x – 2) (x – 3) . . . . . . (x – 100)
= x100 – (1 + 2 + 3 + . . . . . . . + 100) x99 + (. . .) x98 + . . . . . .
Here coeff. Of x99 = -(1 + 2 + 3 + . . . . . . .+ 100)
= -100 x 101/2 = -5050.
Akram Khan
35 Points
3 years ago
(x – 1) (x – 2) (x – 3) . . . . . . (x – 100)= x100 – (1 + 2 + 3 + . . . . . . . + 100) x99 + (. . .) x98 + . . . . . .Here coeff. Of x99 = -(1 + 2 + 3 + . . . . . . .+ 100)= -100 x 101/2 = -5050
ram
13 Points
3 years ago
(x – 1) (x – 2) (x – 3) . . . . . . (x – 100)= x100 – (1 + 2 + 3 + . . . . . . . + 100) x99 + (. . .) x98 + . . . . . .Here coeff. Of x99 = -(1 + 2 + 3 + . . . . . . .+ 100)= -100 x 101/2 = -5050.

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