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Find a polynomial of degree 3 (here ao, a1, a2, a3 are real numbers) such that p(x) = ao + a₁x + a₂x² + 3x³ p(-2) = 49, p(-1) = 10, p(0) = 1, and p(1) = -2.

Find a polynomial of degree 3 (here ao, a1, a2, a3 are real numbers) such that p(x) = ao + a₁x + a₂x² + 3x³ p(-2) = 49, p(-1) = 10, p(0) = 1, and p(1) = -2.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Find a polynomial of degree 3 (here ao, a1, a2, a3 are real numbers) such that p(x) = ao + a₁x + a₂x² + 3x³ p(-2) = 49, p(-1) = 10, p(0) = 1, and p(1) = -2.
Transcribed Image Text:Find a polynomial of degree 3 (here ao, a1, a2, a3 are real numbers) such that p(x) = ao + a₁x + a₂x² + 3x³ p(-2) = 49, p(-1) = 10, p(0) = 1, and p(1) = -2.
Answer The coefficients ao, a1, a2, a3 are found by solving the matrix equation 1-2 4 ao 49 1 1 a1 10 1 0 0 0 a2 1 1 1 1 a3 Row-reducing the corresponding augmented matrix, we find the unique solution ao = 1, a₁ = -2, a₂ = 3, and a3 = 4, so the polynomial is p(x) = 1-2x+3x² - 4x³. =
Transcribed Image Text:Answer The coefficients ao, a1, a2, a3 are found by solving the matrix equation 1-2 4 ao 49 1 1 a1 10 1 0 0 0 a2 1 1 1 1 a3 Row-reducing the corresponding augmented matrix, we find the unique solution ao = 1, a₁ = -2, a₂ = 3, and a3 = 4, so the polynomial is p(x) = 1-2x+3x² - 4x³. =
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