Welcome to the forum.
It is not exactly clear what "can be entered on the form of a polynomial" means. Do you mean that there exists a polynomial and four points such that , , , ? Is there any condition on , for example: , ..., or ?
Hi, I need help with a question regarding sequences and sums:
The upper of the two following sequences can be entered on the form of a polynomial (ie, an = degree 2 polynomial). Prove that the bottom can not be printed in the form of a degree 2 polynomial. (Hint: start by proving that the top can be entered on the form of a degree 2 polynomial).
0 1 4 9
0 1 4 10
The quadratic function, f, such that f(0)= 0, f(1)= 1, f(2)= 4, f(3)= 9 is fairly obvious. If we are to assume that the second function must give f(0)= 0, f(1)= 1, f(2)= 4, f(3)= 10, then the answer is simple since a quadratic function, having 3 coefficients, is determined by 3 equations.