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Original Message (ID '370772') By Bill Simpson:
Here is an example kappa In[1]:= kappa[t_,lambda_]:=lambda^2+t+1; Reduce[kappa[t,lambda]==0,lambda] Out[2]= lambda== -Sqrt[-1-t] || lambda==Sqrt[-1-t] For different definitions of kappa the form of the result may be very different. Thus providing a single simple method of negating that solution seems risky. Manually I can say that your solution would be lambda!= -Sqrt[-1-t] && lambda!=Sqrt[-1-t] is the set of lambda where there are no zeros. Without knowing more about your kappa I don't see a way to say any more than this.