I was asked to solved for the eigenvalues in terms of α for 2X2 matrix and so i did and my answer was marked as correct. Then I was asked to solve for this:
The roots are complex when?
There is a saddle point for?
The equilibrium point is a stable node where?
I tried solving the problem by finding values which would give me 1 and zero for the eigenvalues and got the values of -24/11, -25/11 and -26/11 but the were all wrong. How would i solve for these three questions? can someone walk me through the steps?
The eigenvalues in terms of α are:
$r = -1 + \dfrac{\sqrt{100 + 44 \alpha}}{2}$
$r_2 = -1 - \dfrac{\sqrt{100 + 44 \alpha}}{2}$