Problem with implementing unsteady Kutta condition-Hess and Smith Panel method
 

I have been trying to implement Hess and Smith panel method for unsteady case for my summer project, using the unsteady Kutta condition (Basu and Hancock). Since the Kutta condition is non-linear, i end up with 2 roots.

I'm having a problem on how to choose the roots. If I choose the larger root, the wake panel vorticity obtained is very high and the solution does not converge. If I choose the smaller root, the wake panel vorticity obtained is very small and hence there is no lift generation.

Can anyone guide me as to how the roots have to be chosen in order to arrive at the right solution.

Thanks in advance.