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5. Given the following polynomials: P(x)=32(x+1)+0(x + 1)(x) + (x + 1)(x)(x - 1) and Q(x) = −1 +4(x+2) - 3(x+2)(x + 1) + (x+2)(x+1)(x) == (a) Show that P(x) and Q(x) both interpolate the data Ꮖ f(x) | - -2 - -1 0 2 -1 3 1 - -1 3 (b) Why does part (a) not violate the uniqueness property of interpolating polynomials?

5. Given the following polynomials: P(x)=32(x+1)+0(x + 1)(x) + (x + 1)(x)(x - 1) and Q(x) = −1 +4(x+2) - 3(x+2)(x + 1) + (x+2)(x+1)(x) == (a) Show that P(x) and Q(x) both interpolate the data Ꮖ f(x) | - -2 - -1 0 2 -1 3 1 - -1 3 (b) Why does part (a) not violate the uniqueness property of interpolating polynomials?

C++ for Engineers and Scientists
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter14: Numerical Methods
Section14.3: Refinements To The Bisection Method
Problem 4E
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5. Given the following polynomials: P(x)=32(x+1)+0(x + 1)(x) + (x + 1)(x)(x - 1) and Q(x) = −1 +4(x+2) - 3(x+2)(x + 1) + (x+2)(x+1)(x) == (a) Show that P(x) and Q(x) both interpolate the data Ꮖ f(x) | - -2 - -1 0 2 -1 3 1 - -1 3 (b) Why does part (a) not violate the uniqueness property of interpolating polynomials?
Transcribed Image Text:5. Given the following polynomials: P(x)=32(x+1)+0(x + 1)(x) + (x + 1)(x)(x - 1) and Q(x) = −1 +4(x+2) - 3(x+2)(x + 1) + (x+2)(x+1)(x) == (a) Show that P(x) and Q(x) both interpolate the data Ꮖ f(x) | - -2 - -1 0 2 -1 3 1 - -1 3 (b) Why does part (a) not violate the uniqueness property of interpolating polynomials?
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