Theory of Equations 1 Question 41
42. The coefficient of $x^{99}$ in the polynomial $(x-1)(x-2) \ldots(x-100)$ is….
(1982, 2M)
True/False
Show Answer
Solution:
- The coefficient of $x^{99}$ in $(x-1)(x-2) \ldots(x-100)$
$$ \begin{aligned} & =-(1+2+3+\ldots+100) \\ & =-\frac{100}{2}(1+100)=-50(101)=-5050 \end{aligned} $$
