IGNOU BMTE 144 2026 - Obtain the interpolating polynomial in simplest form which fits the fo

Question

Obtain the interpolating polynomial in simplest form which fits the following data:

x	-1	0	1	2
f(x)	3	-4	5	-6

09 Jan 2026

Answer :

Word Count : 330

We are asked to find the interpolating polynomial for the data (x = -1, 0, 1, 2) with (f(x) = 3, -4, 5, -6) using the Newton forward difference method (or equivalently constructing a polynomial manually). First, construct the divided differences table: | (x) | (f(x)) | (\Delta f) | (\Delta^2 f) | (\Delta^3 f) | | --- | ------ | ---------- | ------------ | ------------ | | -1 | 3 | | | | | 0 | -4 | -7 | | | | 1 | 5 | 9 | 8

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