Explanation

(b)
Applying $R_{2} \rightarrow R_{2} - R_{1},R_{3} \rightarrow R_{3} - R_{1},$we get
$\left| \begin{matrix}
1 & 4 & 20 \\
0 & - 6 & - 15 \\
0 & 2x - 4 & 5x^{2} - 20
\end{matrix} \right|$=0
$\Rightarrow 1\left\lbrack - 6\left( 5x^{2} - 20 \right) + 15(2x - 4) \right\rbrack = 0$
$\Rightarrow x^{2} - x - 2 = 0$
$\Rightarrow (x - 2)(x + 1) = 0$
$\Rightarrow \ \ \ x = - 1,\ 2$