awesauce15

You can start by finding the solutions to $x^2+5x+3$. When you plug that into the quadratic formula, you will end up with $\frac{-5 \pm \sqrt{13}}{2}$.$\left(\frac{-5+\sqrt{13}}{2}\right)^2=38-10\sqrt{13}$ and $\left(\frac{-5-\sqrt{13}}{2}\right)^2=38+10\sqrt{13}$ since those are the solutions to the second quadratic, we know that the second quadratic is the expanded form of $(x-38+10\sqrt{13})(x-38-10\sqrt{13})$. When you expand that, you get $x^2-76x+144$. $b=-76$, and $c=144$, so $b+c=\color{red}{68}$.

Well, you need to use Combinations to solve this problem. You have 6 items, and you need to choose 2. Therefore, you have $6 \choose 2$=15, Thus the answer is $15$. I hope this is what you were looking for.