Why do we multiply x - intercepts when creating polynomial equations?

Question

I understand polynomials and the fact that the solutions to a polynomial equation $ P(x) = x^n+ x^{n-1} + x^{n-2}......$ would be the x intercepts on a normal x-y graph. One question I've always had was why do we multiply the roots to create a equation? This is something I never cared to understand now that i think of it , why would we multiply the roots?

Answer 1

We know that for equation of form y=x^n+x^n-1 etc... The roots are values of x for which y=0. If Kn denotes the nth root .then the equation can be recasted in the form of products. Like y= (x-k1)(x-k2) etc.. * Because if this product form was not possible then y won't be equal to zero when x=kn .