Question

If $f(x) = \left| \begin{matrix} 1 & x & x + 1 \\ 2x & x(x - 1) & x(x + 1) \\ 3x(x - 1) & x(x - 1)(x - 2) & x\left( x^{2} - 1 \right) \end{matrix} \right|$ then f(200) is equal to

• A. 1
• B. 0
• C. 200
• D. -200

Answer 1

Answer: (B)

0

Answer 2

1 & 1 & 1 \\ 2x & x - 1 & x \\ 3x(x - 1) & (x - 1)(x - 2) & x(x - 1) \end{matrix} \right|$$ = $x(x + 1)(x - 1)\left| \begin{matrix} 1 & 1 & 1 \\ 2x & x - 1 & x \\ 3x & x - 2 & x \end{matrix} \right|$ Applying $C_{2} \rightarrow C_{2} - C_{1} C_{3} \rightarrow C_{3} - C_{1}$ ∴ $f(200) = 0$