If \( \begin{vmatrix}x-2 & -3\\3x & 2x\end{vmatrix}=3 \), then the values of \( x \) are:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{1}{2} \) and \( -3 \)
Expanding the determinant:
\( \displaystyle (x-2)(2x)-(-3)(3x)=3 \)
\( \displaystyle 2x^2-4x+9x-3=0 \)
\( \displaystyle 2x^2+5x-3=0 \)
\( \displaystyle (2x-1)(x+3)=0 \)
\( \displaystyle x=\frac{1}{2}\ \text{or}\ x=-3 \)