HA 6, problem 1c of sections 4.1 and 4.2

[Shaghayegh A]

Problem 1c asks to investigate how many negative eigenvalues there are:
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter4/S4.2.P.html#mjx-eqn-a

I understand that we have the hyperbola $$\alpha + \beta+ \alpha \beta l=0$$ which divides the $(\alpha,\beta)$ plane into three zones, as he problem states. But how does that actually help us find the number of negative eigenvalues?

[Victor Ivrii]

Look in the textbook:we just need to calculate the number of eigenvalues at the point of our choice in each region