If \( \begin{vmatrix}6 & 7\\3 & 8\end{vmatrix}=\begin{vmatrix}3x & 6\\-1 & x\end{vmatrix} \), then the sum of values of \( x \) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
Expanding both determinants:
\( 48-21=3x^2+6 \)
\( 3x^2=21 \)
\( x^2=7 \)
\( x=\pm\sqrt{7} \)
The sum of the two values is \( \sqrt{7}+(-\sqrt{7})=0 \).
Why the other options are incorrect
Option (1) 7 — Incorrect. 7 is the value of \( x^2 \), not the sum of the values of x.
Option (2) \( 2\sqrt{7} \) — Incorrect. This adds the values as if both were positive; one of them is \( -\sqrt{7} \).
Option (3) 21 — Incorrect. 21 is the value of \( 3x^2 \), not the sum of the values of x.