Question
Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to
Let $A=\left(\begin{array}{cc}1 & 2 \\ -2 & -5\end{array}\right)$. Let $\alpha, \beta \in \mathbb{R}$ be such that $\alpha A^{2}+\beta A=2 I$. Then $\alpha+\beta$ is equal to