Answer
Two real solutions.
Work Step by Step
We find the discriminant ($a=1, b=r, c=-s$):
$D=b^{2}-4ac=(r)^{2}-4(1)(-s)=r^{2}+4s$
We are told that $s$ is positive and $r^2$ must be positive, so $D$ is posititive. The discriminant is positive, so there are two real solutions.