Assignment:
Alice: "I'm thinking of a polynomial f(x) with non-negative integer coefficients. Can you tell which one?"
Bob: "Well, I need some information."
Alice: "You can pick any real number r and I'll tell you f(r). Um....that is, I'll tell you finitely many digits of f(r) - but as many as you want."
Bob: "Gee - just one value of your polynomial? I dunno...."
Help Bob out. Tell him a good choice for r, and then how he can determine f(x) in finitely many steps.
Provide complete and step by step solution for the question and show calculations and use formulas.