Explanation

(a)
Let $f(x) = \left| \begin{matrix}
1 & 1 & 1 \\
2x & (x - 1) & x \\
3x(x - 1) & (x - 1)(x - 2) & x(x - 1)
\end{matrix} \right|$
$= (x - 1)\left| \begin{matrix}
1 & 1 & 1 \\
2x & x - 1 & x \\
3x & x - 2 & x
\end{matrix} \right|$
Applying $C_{1} \rightarrow C_{1} - C_{3}\ and\ C_{2} \rightarrow C_{2} - C_{3}$
$= (x - 1)\left| \begin{matrix}
0 & 0 & 1 \\
x & - 1 & x \\
2x & - 2 & x
\end{matrix} \right|$
$= (x - 1)\lbrack - 2x + 2x\rbrack = 0$
$\therefore f(x) = 0$
$\Rightarrow f(50) = 0$