Product of Roots of Sums of Products of Differences

Algebra Level 3

What is the product of all roots to the equation

(x1)(x2)(x3)+(x2)(x3)(x4)+(x3)(x4)(x5)+(x4)(x5)(x6)+(x5)(x6)(x7)+(x6)(x7)(x8)=0? \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 "?".


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