Product of All Roots

Algebra Level 3

What is the product of all roots to the equation

\( f(x) = (x-1)(x-2) + (x-2)(x-3) \) \(+ (x-3)(x-4) + (x-4)(x-5) + (x-5)(x-6) \) \(+ (x-6)(x-7) + (x-7)(x-8) + (x-8)(x-9) = 0 ? \)

Details and assumptions

If you think that there are no roots (solutions) to this equation, then your answer would be the empty product, which is 1.

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