What is the product of all roots to the equation
++(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?
If p(x) = an x^n + ...+a0,
then,
p(x) = an (x-r1)(x-r2)....(x-rn)
where the rj are the roots of p(x). The product of all the roots is then related to p(0). Puting x = 0 in the above identity gives:
p(0) = (-1)^n an Product from j = 1 to n of rj
In your case, n = 6 and a6 = 2.