Question

The value of the determinant $\left| \begin{matrix} (x–2)^{2} & (x–1)^{2} & x^{2} \\ (x–1)^{2} & x^{2} & (x + 1)^{2} \\ x^{2} & (x + 1)^{2} & (x + 2)^{2} \end{matrix} \right|$ is –

• A. 8x²
• B. 8
• C. – 8
• D. 0

Answer 1

Answer: (C)

– 8

Answer 2

Put x = 0 in given determinant $\left| \begin{matrix} 4 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 4 \end{matrix} \right|$

= 4 (– 1) – 1 (4) = – 8