Question

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

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

Answer 1

The correct option is A $3,-1$

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