June 10, 2008

If a polynomial of order n or less passes thru (n+1) points, it is unique!

Given n+1 (x,y) data pairs, with all x values being unique, then a polynomial of order n or less passes thru the (n+1) data points. How can we prove that this polynomial is unique?
I am going to show you the proof for a particular case and you can extend it to polynomials of any [...]