Question

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

Answer 1

Answer: 51