Question
Question: The value of 'λ' if ax<sup>4</sup> + bx<sup>3</sup> + cx<sup>2</sup> + 50x + d **=** \(\left| \begi...
The value of 'λ' if ax4 + bx3 + cx2 + 50x + d
= $\left| \begin{matrix} x^{3} - 14x^{2} & - x & 3x + \lambda \ 4x + 1 & 3x & x - 4 \
- 3 & 4 & 0 \end{matrix} \right|$ is
A
0
B
3
C
2
D
1
Answer
2
Explanation
Solution
On differentiating with respect to x
4ax3 + 3bx2 + 2cx + 50
= $\left| \begin{matrix} 3x^{2} - 28x & - 1 & 3 \ 4x + 1 & 3x & x - 4 \
- 3 & 4 & 0 \end{matrix} \right|+\left| \begin{matrix} x^{3} - 14x^{2} & - x & 3x + \lambda \ 4 & 3 & 1 \
- 3 & 4 & 0 \end{matrix} \right|$
Put x = 0
50 = $\left| \begin{matrix} 0 & - 1 & 3 \ 1 & 0 & - 4 \
- 3 & 4 & 0 \end{matrix} \right|+\left| \begin{matrix} 0 & 0 & \lambda \ 4 & 3 & 1 \
- 3 & 4 & 0 \end{matrix} \right|$
50 = 25λ ⇒ λ = 2