Question

The solutions of the equation $\begin{vmatrix} x & 2& -1 \\\[0.3em] 2 & 5 & x \\\[0.3em] -1 & 2& 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

$\begin{vmatrix} x & 2& -1 \\\[0.3em] 2 & 5 & x \\\[0.3em] -1 & 2& x \end{vmatrix}=0$
$\Rightarrow \begin{vmatrix} x & 2& -1 \\\[0.3em] 2 & 5 & x \\\[0.3em] -3 & -3& 0 \end{vmatrix}=0\, R_3 \rightarrow R_3-R_2$
$\Rightarrow-1(-6+15)-x[-3 x+6]=0$
$\Rightarrow-9+3 x^{2}-6 x=0$
$\Rightarrow x^{2}-2 x-3=0$
$\Rightarrow(x-3)(x+1)=0$
$\Rightarrow x=-1,3$