A) 2, 7
B) - 2, 7
C) 2, -7
D) - 2, -7
Correct Answer: A
Solution :
\[\left| \,\begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{matrix}\, \right|\,=0\]\[\Rightarrow \] \[(x+9)\,\left| \,\begin{matrix} 1 & 1 & 1 \\ 2 & x & 2 \\ 7 & 6 & x \\ \end{matrix}\, \right|=0\],by \[{{R}_{1}}\to {{R}_{1}}+{{R}_{2}}+{{R}_{3}}\] \[\Rightarrow \] \[(x+9)\,\{({{x}^{2}}-12)-(2x-14)+(12-7x)\}=0\] \[\Rightarrow \] \[(x+9)\,({{x}^{2}}-9x+14)=0\] \[\Rightarrow (x+9)(x-2)\,(x-7)=0\] Hence the other two roots are\[x=2,\,7\].
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