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Vieta's formula relates the coefficients of polynomials to the sum and products of their roots. This can provide a shortcut to finding solutions in more complicated algebraic polynomials.

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

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What is the product of all roots to the equation

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

**Details and assumptions**

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

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