Algebra

First, let's write a quadratic equation to find the two roots. 

We have \(x^{2}+9x-20=0\)

 

Notice that \(r^2 + s^2 = (r+s)^2-2rs\). 

 

Now, let's take a break from this. If we had roots r and s, we would have

\((x-r)(x-s)\\ x^2-sx-rx+rs\\ x^2-(r+s)x+rs\)

 

Using the equation from above, we find that, r+s is equal to -9 and rs is equal to -20. 

 

Plugging that in to \( (r+s)^2-2rs\), we get\((-9)^2-2(-20) = 81+40 = 121\)

 

So 121 is our answer!

 

Thanks! :)\(\)