Question

A root of the equation $\left| \begin{matrix} 3 - x & - 6 & 3 \

• 6 & 3 - x & 3 \ 3 & 3 & - 6 - x \end{matrix} \right| = 0$is.

• A. 6
• B. 3
• C. 0
• D. None of these

Answer 1

Answer: (C)

0

Answer 2

Applying $C_{1} \rightarrow C_{1} + C_{2} + C_{3}$, we obtain

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

1 & - 6 & 3 \\ 0 & 9 - x & 0 \\ 0 & 9 & - 9 - x \end{matrix} \right| = 0$$ $\Rightarrow - x(9 - x)( - 9 - x) = 0 \Rightarrow x = 0,9, - 9$. **Trick :** Check by assuming the values of x from the given options.