A) 0
B) 1
C) 100
D) \[-100\]
Correct Answer: A
Solution :
\[f(x)=\] \[\left| \begin{matrix} 1 & x & x+1 \\ 2x & x(x-1) & (x+1)x \\ 3x(x-1) & x(x-1)(x-2) & (x+1)x(x-1) \\ \end{matrix} \right|\] Applying\[{{R}_{3}}\to {{R}_{3}}-({{R}_{1}}+{{R}_{2}})\] \[=\left| \begin{matrix} 1 & x & 0 \\ 2x & x(x-1) & 0 \\ 3x(x-1) & x(x-1)(x-2) & 0 \\ \end{matrix} \right|=0\] \[\therefore \] \[f(x)=0\Rightarrow f(100)=0\]You need to login to perform this action.
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