That is, as you have been told, impossible. If you multiply both sides of
by x you get
which is a
quadratic equation and has, at most, 2 distinct roots. The original equation might have fewer solutions, but cannot have more so NO value of q gives the equation 4 roots.
If, on the other hand, you are saying that 4
is a root, we must have
so that
and then
.
What is the exact statement of the problem in your text? You posted a picture in your first post, but that is something you wrote. Could you post a picture of the problem in the text?