Question

The solutions of the equation $\left|\begin{array}{ccc}x& 2& -1\\ 2& 5& x\\ -1& z& x\end{array}\right|=0$ are

• A. 3,-1
• B. -3,1
• C. 3,1
• D. -3,-1

Answer 1

Answer: (A)

Since, $\left|\begin{array}{ccc}x& 2& -1\\ 2& 5& x\\ -1& 2& x\end{array}\right|=0$
$\Rightarrow \left|\begin{array}{ccc}x& 2& -1\\ 2& 5& x\\ -3& -3& 0\end{array}\right|=0$
$R_3\to R_3-R_2$
$\Rightarrow -1(-6+15)-x[-3x+6]=0$
$\Rightarrow -9+3x^2-6x=0$
$\Rightarrow x^2-2x-3=0$
$\Rightarrow (x-3)(x+1)=0$
$x=-1,3$