Algebra
# Vieta's Formula

Given that 2 roots of $f(x) = x^3 + ax + b$ are 2 and 7, what is $a+b$?

What is the product of all roots to the equation

$\begin{aligned} & (x-1)(x-2)(x-3) + (x-2)(x-3)(x-4) \\ + & (x-3)(x-4)(x-5) + (x-4)(x-5)(x-6) \\ + & (x-5)(x-6)(x-7) + (x-6)(x-7)(x-8) =0 ? \end{aligned}$

**Details and assumptions**

Clarification: Make sure you scroll to the right (if need be) to see the full equation. This problem ends with a "?".