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)

3,-1

Answer 2

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