Question

The solutions of the equation $\begin{vmatrix} {x}&{2} &{-1}\\ {2}&{5}& {x} \\ {-1}&{z}&{x}\\ \end{vmatrix} =0$ are

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

Answer 1

Answer: (A)

Since, $\begin{vmatrix}x & 2 & -1 \\ 2 & 5 & x \\ -1 & 2 & x\end{vmatrix}=0 $
$\Rightarrow \begin{vmatrix} x & 2 & -1 \\ 2 & 5 & x \\ -3 & -3 & 0\end{vmatrix}=0$
$R_{3} \rightarrow R_{3}-R_{2}$
$\Rightarrow -1(-6+15)-x[-3 x+6]=0$
$\Rightarrow \,-9+3 x^{2}-6 x=0$
$\Rightarrow \,x^{2}-2 x-3=0$
$\Rightarrow \,(x-3)(x+1)=0$
$x=-1,3$