A) 0 and\[-6\]
B) 0 and 6
C) 6
D) \[-6\]
E) \[0\]
Correct Answer: A
Solution :
\[\left| \begin{matrix} x+1 & 1 & 1 \\ 2 & x+2 & 2 \\ 3 & 3 & x+3 \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[\left| \begin{matrix} x+6 & x+6 & x+6 \\ 2 & x+2 & 2 \\ 3 & 3 & x+3 \\ \end{matrix} \right|=0\] \[({{R}_{1}}\to {{R}_{1}}+{{R}_{2}}+{{R}_{3}})\] \[\Rightarrow \] \[(x+6)\left| \begin{matrix} 1 & 0 & 0 \\ 2 & x & 0 \\ 3 & 0 & x \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[(x+6){{x}^{2}}=0\] \[\Rightarrow \] \[x=0,-6\]
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