Exercise 47 (a) Show that there exists a unique polynomial po of degree < 2 such that po(-1) = 1, po(0) = -1 and po(1) = -1. (b) Show that a polynomial q(2) E P(R) such that q(-1) = q(0) = q(1) = 0 is divisible by z (c) Find all polynomials p E P(R) (any degree) such that p(-1) = 1, p(0) P(1) = -1. %3D -2. = -1 and
Exercise 47 (a) Show that there exists a unique polynomial po of degree < 2 such that po(-1) = 1, po(0) = -1 and po(1) = -1. (b) Show that a polynomial q(2) E P(R) such that q(-1) = q(0) = q(1) = 0 is divisible by z (c) Find all polynomials p E P(R) (any degree) such that p(-1) = 1, p(0) P(1) = -1. %3D -2. = -1 and
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercise 47 -
such that po(-1) = 1, po(0) = -1 and po(1) = -1.
(b) Show that a polynomial q(2) E P(R) such that q(-1) = q(0) = q(1) = 0 is divisible
by 2
(c) Find all polynomials p E P(R) (any degree) such that p(-1) = 1, p(0)
p(1) = -1.
(a) Show that there exists a unique polynomial po of degree < 2
%3D
-2.
= -1 and
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