Question

If $\alpha$ and $\beta$ are roots of the equation $\begin{bmatrix}1 & 25\end{bmatrix}\begin{bmatrix}0 & \frac{1}{2} \\ -1 & \frac{1}{2}\end{bmatrix}^5\begin{bmatrix}0 & \frac{1}{2} \\ -1 & \frac{1}{2}\end{bmatrix}^5\begin{bmatrix}x^2-5 x+20 \\ x+2\end{bmatrix}=\begin{bmatrix}40\end{bmatrix}$ then find the value of $(1-\alpha)(1-\beta)$

Answer 1

Correct answer is '51'