Question

If x $\ne 0$ and $\left|\begin{array}{ccc}1& x& 2x\\ 1& 3x& 5x\\ 1& 3& 4\end{array}\right|$ =0 , then x =

• A. 1
• B. -1
• C. 2
• D. -2

Answer 1

Answer: (B)

-1

$\Rightarrow \left|\begin{array}{ccc}1& x& 2x\\ 1& 3x& 5x\\ 1& 3& 4\end{array}\right|=0$
$\Rightarrow (12x-15x)-x[4-5x]+2x[3-3x]=0$
$\Rightarrow -3x-4x+5x^2+6x-6x^2=0$
$\Rightarrow -x^2-x=0$
$\Rightarrow x(x+1)=0$
Given $x\ne 0$ [given]
So $x=-1$