Example to show that a polynomial of order n or less that passes through (n+1) data points is unique.

Problem: Through three data pairs (0,0), (3,9) and (4,12), an interpolating polynomial of order 2 or less is found to be y=3x. Prove that there is no other polynomial of order 2 or less that passes through these three points.

See the pdf file for solution.

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