If $A = \begin{bmatrix} 4 & 3 \\ 2 & 5 \end{bmatrix}$, find $x$ and $y$ such that $A^2-xA+yI=0.$

Question

$\begin{array}{1 1} x = 9,y = 4 \\ x = 7,y = 14 \\ x = 9,y = -14 \\ x = 9,y = 14 \end{array}$