I am doing a project on differential equations and stability analysis on economic models.
However I am stuck doing inequalities for the stability analysis. My source is giving these conditions for the domain, underlined in red, to be stable, and I am just not able to tell how these inequalities arise. The eigenvalues for the system are as follows
$$\rho_{1,2}=\frac{1}{2}\left(\left(\alpha-\frac{1}{\beta}\right)\pm\sqrt{\left(\alpha+\frac{1}{\beta}\right)^2-4}\right)$$
And the condition of stability for this system is $0>\rho_1>\rho_2$ as in the picture.
I have been trying for a long time to figure this out, any help is appreciated, thanks.