Question

If $\left| \begin{matrix} x^{3} + 4x & x + 3 & x - 2 \\ x - 2 & 5x & x - 1 \\ x - 3 & x + 2 & 4x \end{matrix} \right|$ = ax⁵ + bx⁴ + cx³ + dx² + ex + f be an identity in x, where a, b, c, d, e, f are independent of x, then the value of f is –

• A. 0
• B. 15
• C. 17
• D. None of these

Answer 1

Answer: (C)

17

Answer 2

Putting x = 0,

$\left| \begin{matrix} 0 & 3 & - 2 \

• 2 & 0 & - 1 \
• 3 & 2 & 0 \end{matrix} \right|$ = f

or f = 17