Homework Help is Here – Start Your Trial Now!
Math
Algebra
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,...
See similar textbooks
Question
100%
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. =
Expert Solution
steps

Step by step

Solved in 5 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS