Question

If $\left|\begin{array}{ccc}1+x& 2& 3\\ 1& 2+x& 3\\ 1& 2& 3+x\end{array}\right|=0$ then $x=$

• A. $1$
• B. $-1$
• C. $-6$
• D. $6$

Answer 1

The correct option is A $1$

We have $(1-x)\left(\right(2+x\left)\right(3+x)-6)-2(3-2)+3(2-(2+x\left)\right)=0$

it gives $6x^2+x^3=0$

$x^2(6+x)=0⟹x=0,0,-6$

option c gives correct answer