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?

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

Question

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

anonymous · Answer

this is a quadratic with leading coefficient 9 i believe

anonymous · Answer

no sorry with leading coefficient 8

anonymous · Answer

the constant is whatever it is, and the product of the roots is $\frac{c}{a}$ where $c$ is the constant and $a$ is the leading coefficient

anonymous · Answer

$$2+6+12+20+30+42+56+72=240$$ divide by 8

anonymous · Answer

btw the roots are complex, but that doesn't mean you can't multiply them together

anonymous · Answer

thank u

anonymous · Answer

YW