Question

Which of the following is not the root of the equation $\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0$?

• A. 2
• B. 0
• C. 1
• D. -3

Answer 1

The correct option is B 0

$\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0$
$R_1\to R_1-R_2,R_2\to R_2-R_3$
$\left|\begin{array}{ccc}x-2& 3(x-2)& -(x-2)\\ 5& -5x& -5\\ -3& 2x& x+2\end{array}\right|=0$
$5(x-2)\left|\begin{array}{ccc}1& 3& -1\\ 1& -x& -1\\ -3& 2x& x+2\end{array}\right|=0$
$R_1\to R_1-R_2$
$5(x-2)\left|\begin{array}{ccc}0& x+3& 0\\ 1& -x& -1\\ -3& 2x& x+2\end{array}\right|=0$
$-5(x-2)(x+3)(x-1)=0$
$\Rightarrow x=2,1,-3$
Hence, $x=0$ is not a root.