Product of All Roots

Algebra Level 4

What is the product of all roots to the equation

f(x)=(x1)(x2)+(x2)(x3) f(x) = (x-1)(x-2) + (x-2)(x-3) +(x3)(x4)+(x4)(x5)+(x5)(x6)+ (x-3)(x-4) + (x-4)(x-5) + (x-5)(x-6) +(x6)(x7)+(x7)(x8)+(x8)(x9)=0?+ (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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