If
$f(x)= \begin{vmatrix}1 & x & x+1\\2x& x(x-1) & (x+1)x\\ 3x(x-1) & (x-1)(x-2) & (x+1) x(x-1)\end{vmatrix}$
then f(100) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : 0
We have,
$f(x) = \begin{vmatrix}1 & x & x+1\\2x& x(x-1) & (x+1)x\\ 3x(x-1) & (x-1)(x-2) & (x+1) x(x-1)\end{vmatrix}$
Applying $C_3→C_3-C_2, $ we get
$f(x) = \begin{vmatrix}1 & x & 1\\2x& x(x-1) & 2x\\ 3x(x-1) & x(x-1)(x-2) & 3x(x-1)\end{vmatrix}=0$
$∴f(100)= 0.$