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Prove that if a polynomial function p(x)= a + ax + ₂x² is zero for x=-1, x-0, and x-1, then a - a₂ -₂ -0. Getting Started: Write a system of linear equations and solve the system for a, a, and a (1) Substitute x-1, 0, and 1 into p(x). (1) Set the result equal to 0. p(-1) - p(0) - P(1) - -0 -0 (1) Solve the resulting system of linear equations in the variables a, a, and a.

Prove that if a polynomial function p(x)= a + ax + ₂x² is zero for x=-1, x-0, and x-1, then a - a₂ -₂ -0. Getting Started: Write a system of linear equations and solve the system for a, a, and a (1) Substitute x-1, 0, and 1 into p(x). (1) Set the result equal to 0. p(-1) - p(0) - P(1) - -0 -0 (1) Solve the resulting system of linear equations in the variables a, a, and a.

Advanced Engineering Mathematics
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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Prove that if a polynomial function p(x) = ª₂ + ax + a₂x² is zero for x=-1, x=0, and x-1, then a₂-a₁-a₂ -0. Getting Started: Write a system of linear equations and solve the system for a, a, and a₂. (1) Substitute x-1, 0, and 1 into p(x). (11) Set the result equal to 0. p(-1) - <-0 p(0) - p(1) = -D -0 (III) Solve the resulting system of linear equations in the variables a, a, and a₂. (2₂.2₂.2₂) -
Transcribed Image Text:Prove that if a polynomial function p(x) = ª₂ + ax + a₂x² is zero for x=-1, x=0, and x-1, then a₂-a₁-a₂ -0. Getting Started: Write a system of linear equations and solve the system for a, a, and a₂. (1) Substitute x-1, 0, and 1 into p(x). (11) Set the result equal to 0. p(-1) - <-0 p(0) - p(1) = -D -0 (III) Solve the resulting system of linear equations in the variables a, a, and a₂. (2₂.2₂.2₂) -
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