Question

One root of the equation $\left|\begin{array}{ccc}3-x& -6& 3\\ -6& 3-x& 3\\ 3& 3& -6-x\end{array}\right|=0$ is

• A. 6
• B. 3
• C. 0
• D. none

Answer 1

The correct option is C 0

$C_1\to C_1+C_2+C_3$

$\left|\begin{array}{ccc}-x& -6& 3\\ -x& 3-x& 3\\ -x& 3& -6-x\end{array}\right|=0$

$\Rightarrow x\left|\begin{array}{ccc}-1& -6& 3\\ -1& 3-x& 3\\ -1& 3& -6-x\end{array}\right|=0$

$\Rightarrow x=0$