or certainly work. Note that these values belong to . and are not the whole answer because when the denominator factors into , and don't have to be integer.

I am not sure I understand. Under what conditions would x be 0? The question was about the possible values of k.If the equation were to have no vertical asymptote, wouldn't x simply equal x=0?

The graph of has vertical asymptotes, where , iff has roots, so all you need is to examine the discriminant of this quadratic equation.