If pλ4+qλ3+rλ2+sλ+t=∣λ2+3λλ−1λ+3λ2+12−λλ−3λ2−3λ+43λ∣p\lambda^4 + q\lambda^3 + r\lambda^2 + s\lambda + t = \begin{vmatrix} \lambda^2 + 3\lambda & \lambda - 1 & \lambda + 3 \\ \lambda^2 + 1 & 2 - \lambda & \lambda - 3 \\ \lambda^2 - 3 & \lambda + 4 & 3\lambda \end{vmatrix}…

Mathematics

Problem

If pλ4+qλ3+rλ2+sλ+t=∣λ2+3λλ−1λ+3λ2+12−λλ−3λ2−3λ+43λ∣p\lambda^4 + q\lambda^3 + r\lambda^2 + s\lambda + t = \begin{vmatrix} \lambda^2 + 3\lambda & \lambda - 1 & \lambda + 3 \\ \lambda^2 + 1 & 2 - \lambda & \lambda - 3 \\ \lambda^2 - 3 & \lambda + 4 & 3\lambda \end{vmatrix} , then tt is equal to a. 7 b. 14 c. 21 d. 28

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