5. Suppose $f$ is a second-degree polynomial for which $f(2)=1, f(4)=2$, and $f(8)=3$. Find the sum of the roots of $f$.
Answer: 18
Solution: Let $f(x)=a x^{2}+b x+c$. By substituting $x=2,4,8$ we get the system of linear equations
$$
\begin{array}{r}
4 a+2 b+c=1 \\
16 a+4 b+c=2 \\
64 a+8 b+c=3 .
\end{array}
$$

Solving this system of equations gives us $a=-\frac{1}{24}, b=\frac{3}{4}, c=-\frac{1}{3}$. By using Vieta's identities, the sum of roots is $-\frac{b}{a}=\frac{3}{4} \cdot 24=18$.