Show that the Newton divided-difference polynomials 3 — 2(х + 1) + 0(х + 1)х + (x + 1)x(х — 1) and -1+ 4(x + 2) - 3(x + 2)(x + 1) + (x + 2)(x + 1)x - both interpolate the data (-2, –1), (-1,3), (0,1), (1, -1), (2,3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?

Show that the Newton divided-difference polynomials 3 — 2(х + 1) + 0(х + 1)х + (x + 1)x(х — 1) and -1+ 4(x + 2) - 3(x + 2)(x + 1) + (x + 2)(x + 1)x - both interpolate the data (-2, –1), (-1,3), (0,1), (1, -1), (2,3). Why do the polynomials not violate the uniqueness property of interpolating polynomials?

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section4.2: Complex Solutions Of Equations

Problem 6ECP: Find a fourth-degree polynomial function f with real coefficients that has 2, 2, and 7i as zeros.

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