There is a computer that generates a polynomial P(x) of arbitrary degree and positive integer coefficients. You are only allowed to enter inputs for the polynomial P(x) into the computer; the computer will print out the result. So if 2 is your input, the computer prints out the numeric value P(2). This is a theoretical computer and thus numerical accuracy is not something to worry about. What is the minimum no. of inputs before you can completely determine the Polynomial. It goes without saying that the answer is a finite no.
My formulas are: y=(x+a)^2 x=(-y+a)^2 I would like to solve for a where they touch (exact solution). Here is a graph demonstrating what I mean: As you can see, I have attempted to solve for a by making them closer and closer. I think 1.100917368760402698 ≤ a ≤ 1.100917368760402699, but floating point error may have reduced the accuracy of that range, but it should be near those numbers at least. There will also be a negative solution of a , which will be exactly negative I believe.