Question

In the polynomial $(x-1)(x-2)(x-3)...(x-100),$ the coefficient of $x^{99}$ is .

• A. 5050
• B. $-5050$
• C. 100
• D. 99

Answer 1

The correct option is B $-5050$

Given polynomial, $(x-1)(x-2)(x-3)...(x-100)$

Number of terms $=100$

Coefficient of $x^{99}$ in $(x-1)(x-2)(x-3)...(x-100)$

$=(-1-2-3-..........-100)=-(1+2+.........+100)$

$=-\frac{100\times 101}{2}=-5050$