If \( \begin{vmatrix}3 & x\\x & 1\end{vmatrix}=\begin{vmatrix}3 & 2\\4 & 1\end{vmatrix} \) , then value of \( x \) is/are
(A) \( x=2 \)
(B) \( x=-2 \)
(C) \( x=2\sqrt{2} \)
(D) \( x=-2\sqrt{2} \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C) and (D) only
Expanding both determinants,
\( \displaystyle 3-x^2=3-8 \)
\( \displaystyle x^2=8 \)
\( \displaystyle x=\pm 2\sqrt{2} \)
So x = 2√2 or x = −2√2, the two values with \( x^2=8 \).
Checking the statements
(A) \( x=2 \) — Incorrect. Then \( x^2=4\ne 8 \).
(B) \( x=-2 \) — Incorrect. Then \( x^2=4\ne 8 \).
(C) \( x=2\sqrt{2} \) — Correct. Then \( x^2=8 \).
(D) \( x=-2\sqrt{2} \) — Correct. Then \( x^2=8 \).
Tip: Taking x = 2 comes from equating the (1, 2) entries, as if the determinants were matrices. Determinants are equal only in value, not entry by entry.
NCERT (2026-27 edition):
Determinants
