Matrix Power Equation and Constants

Let $A=\begin{bmatrix}1&0&0\\0&2&0\\3&0&-1\end{bmatrix}$ satisfy $A^{20}+\alpha A^{19}+\beta A=\begin{bmatrix}1&0&0\\0&4&0\\0&0&1\end{bmatrix}$ for some real numbers $\alpha$ and $\beta$. Then $\beta-\alpha$ is equal to ______.