Solve this

(d) none of these

$\Delta=\mid \begin{array}{lll}x & 2 & x\end{array}$

$x^{2} \quad x \quad 6$

$\begin{array}{lll}x & x & 6\end{array}$

$=x \mid x \quad 6$

$\begin{array}{ll}x & 6\left|-x^{2}\right| 2 x \\ x & 6|+x| 2 x\end{array}$

$\begin{array}{ll}x & 6\end{array}$           [Expanding along $C_{1}$ ]

$=0-x^{2}\left(12-x^{2}\right)+x\left(12-x^{2}\right)$

$=x^{4}-12 x^{2}+12 x-x^{3}$

$\Delta=a x^{4}+b x^{3}+c x^{2}+d x+e$             [Given]

$\Rightarrow x^{4}-12 x^{2}+12 x-x^{3}=a x^{4}+b x^{3}+c x^{2}+d x+e$

$\Rightarrow a=1, b=-1, c=-12, d=12, e=0$

Thus,

$5 a+4 b+3 c+2 d+e=5-4-36+24+0=-11$