Let p(x) be a quadratic polynomial such that distinct reals a and b ,. p(a)=a and p(b)=b then find the roots of. p[p(x)]-x=0
One set of roots is 'a' and 'b'. What are the other two roots and what is the process of solving for them?
technically, you could expand [p(p(x)) - 1], then try and divide it by (x-a)(x-b), but I suspect there would be a more elegant way of finding the remaining roots.
Does anyone have any solutions?
(I know someone had asked this question earlier, but the solution for the additional two roots was not provided. Therefore I am posting this again.)