Question

The sum of real roots of the equation $\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0,$ is equal to :

• A. $-4$
• B. $0$
• C. $1$
• D. $6$

Answer 1

The correct option is B $0$

$\left|\begin{array}{ccc}x& -6& -1\\ 2& -3x& x-3\\ -3& 2x& x+2\end{array}\right|=0,$

Expanding along row 1

$\Rightarrow x(-3x\times (x+2)-2x(x-3\left)\right)-(-6)\left(2\right(x+2)+3(x-3\left)\right)+(-1)(4x+3(-3x\left)\right)=0$
$\Rightarrow -5x^3+30x-30+5x=0$
Sum of roots$=0$