If p λ 4 + q λ 3 + r λ + 5 λ + t = ∣ ∣ ∣ ∣ λ 2 + 3 λ λ − 1 λ + 3 λ + 1 2 − λ λ − 4 λ − 3 λ + 4 3 λ ∣ ∣ ∣ ∣ , the value of t is Options: A . &nbsp16 B . &nbsp18 C . &nbsp17 D . &nbsp19

If pλ4+qλ3+rλ+5λ+t=∣∣ ∣∣

Question

p λ^{4} + q λ^{3} + r λ + 5 λ + t = ∣ ∣∣ ∣ \begin{matrix} λ^{2} + 3 λ & λ - 1 & λ + 3 λ + 1 & 2 - λ & λ - 4 λ - 3 & λ + 4 & 3 λ \end{matrix} ∣ ∣∣ ∣

, the value of t is

Options:

A . 16

B . 18

C . 17

D . 19

Answer: Option B
:
B
Since it is an identity in

λ

so satisfied by every value of

λ

. Now put

λ = 0

in the given equation, we have

t = ∣ ∣∣ ∣ \begin{matrix} 0 & - 1 & 3 1 & 2 & - 4 - 3 & 4 & 0 \end{matrix} ∣ ∣∣ ∣ = - 12 + 30 = 18

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