Why do I generally see real solutions to recurrence relations?

Question

I haven't worked very much with recurrence relations, but for the ones I have worked with I always get real solutions, which is strange to me because looking briefly at the procedure for solving (linear) recurrence relations, it seems that we try to "find the roots that fit the polynomial". Why should this necessarily give real solutions, or is that just what intro discrete math books do- choose the coefficients to the recurrence relations to yield real solutions?