Consider two distinct polynomials of degree N:

A(X) = a0 + a1*X + a2*X^2 + … + aN*X^N

B(X) = b0 + b1*X + b2*X^2 + … + bN*X^N

where ak and bk are real numbers. Suppose that at X = 1, 2, ..., N, the graphs of A(X) and B(X) intersect.

Questions:

1.) At what places besides X = 1, 2, ..., N do the graphs of A and B intersect?

2.) What is (a0 – b0)/(aN – bN) ?