Pick a value for lambda (1,2,3,...). Since this is multiple choice, you should be able to eliminate the wrong choices (plot the graphs).
In general, for a family of polynomials:
if is a root of and then, is a root of . So, finding a root of and substituting: , we obtain a sufficient condition for .
That is a pity, if were a root of (it isn't) then,
Possiibly (of course I'm not sure) there is typo.
Fernando Revilla