Problem (Algebra):
Let $T=8$. Let $f(x)=a x^{2}+b x+c$. The product of the roots of $f$ is $T$. If $(-2,20)$ and $(1,14)$ lie on the graph of $f$, compute $a$.

Solution:
Using Vièta's Formula, write $f(x)=a x^{2}+b x+T a$. Substituting the coordinates of the given points yields the system of equations: $4 a-2 b+T a=20$ and $a+b+T a=14$. Multiply each side of the latter equation by 2 and add the resulting equation to the former equation to eliminate $b$. Simplifying yields $a=\frac{16}{T+2}$. With $T=8, a=8 / 5$.

Final answer: $\frac{8}{5}$