Answer
This equation has two distinct real solutions.
Work Step by Step
$x^{2}+rx-s=0$ $(s\gt0)$
The formula for the discriminant is $D=b^{2}=4ac$. For this equation, $a=1$, $b=r$ and $c=-s$
Substitute the known values in the formula:
$D=r^{2}-4(1)(-s)=r^{2}+4s$
We can be sure $r^{2}$ is a positive number, because any real number squared produces a positive number, and since we know $s\gt0$, then we can be certain that $r^{2}+4s$ is also a positive number.
Knowing these facts, we can say that $D\gt0$ and that means that this equation has two distinct real solutions.
