If \( \begin{vmatrix}2x & 2\\8 & x\end{vmatrix}=\begin{vmatrix}-4 & -2\\4 & -2\end{vmatrix} \) then \( x \) =
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ±4
Expanding both determinants:
\( \displaystyle 2x\cdot x-2\cdot 8=(-4)(-2)-(-2)(4) \)
\( \displaystyle 2x^2-16=16 \)
\( \displaystyle 2x^2=32 \)
\( \displaystyle x^2=16 \)
\( \displaystyle x=\pm 4 \)
Why the other options are incorrect
Option (1) 4 — Incorrect. x = 4 is a solution, but x = −4 also satisfies \( x^2=16 \); taking only the positive root loses a solution.
Option (3) −2 — Incorrect. With x = −2 the left side is 2(4) − 16 = −8, not 16.
Option (4) −4 — Incorrect. x = −4 is a solution, but x = 4 is also a solution.