Question

Let p(x) be a polynomial with positive integers conefficients. You can ask the question: What is p(n) for any positive integer n? What is the minimum number of questions to be asked to determine p(x) completely?Justify.

Answer 1

For people who know about simultaneous equations:
Let \(p(x)=\sum_{i=0}^n {a_ix^i}\)
Then we have to know n+1 unknown constants, \(a_0,\ldots,a_n\).
So we need to solve n+1 equations.
\(\therefore\) we need to ask n+1 questions.
But there's a problem. We don't know the degree of the polynomial.
So the answer is there's no way of determining p(x) completely.

Answer 2

That is a pretty straightforward method and a nice try :)

Answer 3

But the correct answer is "two questions"

Answer 4

Is it a riddle? :/

Answer 5

Haha not a riddle, it is a regular math problem..

Answer 6

Am I mistaken the problem?

Answer 7

In your method, you're not using "all" the given information

Answer 8

It is given that the coefficients of the polynomial are "positive integers"

you haven't used that info anywhere

Answer 9

I thought it won't matter.

Answer 10

It don't matter whether \(a_i\)s are positive integers or not.

Answer 11

would it be n questions?

Answer 12

wait 2 questions really for alll n?

Answer 13

even for an infinite polynomial

Answer 14

Yes

Answer 15

For an analogy, consider the following quick example