Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}\mathrm{x} & 3 & 7 \\ 2 & \mathrm{x} & 2 \\ 7 & 6 & \mathrm{x}\end{array}\right|=0$ is A. $\{2,-3.7\}$ B. $\{2,7 .-9\}$ C. $[-2,3,-7\}$ D. none of these

Home » Mark the tick against the correct answer in the following: The solution set of the equation is A. B. C. D. none of these

Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}\mathrm{x} & 3 & 7 \\ 2 & \mathrm{x} & 2 \\ 7 & 6 & \mathrm{x}\end{array}\right|=0$ is
A. $\{2,-3.7\}$
B. $\{2,7 .-9\}$
C. $[-2,3,-7\}$
D. none of these

CBSE | Class 12 | Determinants | Maths | RS Aggarwal

Mark the tick against the correct answer in the following: The solution set of the equation $\left|\begin{array}{ccc}\mathrm{x} & 3 & 7 \\ 2 & \mathrm{x} & 2 \\ 7 & 6 & \mathrm{x}\end{array}\right|=0$ is
A. $\{2,-3.7\}$
B. $\{2,7 .-9\}$
C. $[-2,3,-7\}$
D. none of these

Solution:

Option(C)
To find: Value of $x$
We have, $\left|\begin{array}{lll}\mathrm{x} & 3 & 7 \\ 2 & \mathrm{X} & 2 \\ 7 & 6 & \mathrm{x}\end{array}\right|=0$
Applying $\mathrm{R}_{1} \rightarrow 2 \mathrm{R}_{1}$
$\Rightarrow\left|\begin{array}{ccc} 2 x & 6 & 14 \\ 2 & x & 2 \\ 7 & 6 & x \end{array}\right|=0$
Applying $\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}-\mathrm{R}_{3}$
$\Rightarrow\left|\begin{array}{ccc} 2 x-7 & 0 & 14-x \\ 2 & x & 2 \\ 7 & 6 & x \end{array}\right|=0$
Expanding along $R_{1}$
$\Rightarrow[(2 x-7)\{(x)(x)-(6)(2)\}+(14-x)\{(2)(6)-(x)(7)]=0$
$\begin{array}{l} \Rightarrow\left[(2 x-7)\left\{x^{2}-12\right\}+(14-x)\{12-7 x\}\right]=0 \\ \Rightarrow\left[2 x^{3}-24 x-7 x^{2}+84+168-98 x-12 x+7 x^{2}\right]=0 \\ \Rightarrow\left[2 x^{3}-134 x+252\right]=0 \\ \Rightarrow\left[x^{3}-67 x+126\right]=0 \end{array}$
By Hit and trial $x=-2,3,-7$