SOLUTION: Give an example of polynomials p and q of degree 3 such that p(1) = q(1), p(2) = q(2), and p(3) = q(3), but p(4) is not equal to q(4).

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Give an example of polynomials p and q of degree 3 such that p(1) = q(1), p(2) = q(2), and p(3) = q(3), but p(4) is not equal to q(4).      Log On


   

Question 948077: Give an example of polynomials p and q of degree 3
such that p(1) = q(1), p(2) = q(2), and p(3) = q(3),
but p(4) is not equal to q(4).
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Given: p(x) - q(x) = 0 has roots at x = 1, 2, 3

Therefore p(x) - q(x) = C(x-1)(x-2)(x-3) for constant C.

To simplify things, let C = 1. We can pick any cubic polynomials p, q with degree 3 that satisfy the constraint. A simple example is to let

p(x) = (x-1)(x-2)(x-3) + x^3
q(x) = x^3

Then p(i) = q(i) for i = 1,2,3, but p(4) = 70 and q(4) = 64.