Find a polynomialof degree 3 (here ao, a1, a2, a3 are real numbers) such thatp(x) = ao + a₁x + a₂x² + 3x³p(-2) = 49, p(-1) = 10, p(0) = 1, and p(1) = -2. AnswerThe coefficients ao, a1, a2, a3 are found by solving the matrix equation1-24ao4911a110100 0a2111 1a3Row-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.=

This question can be solved using the concept of solving system of linear equation using matrix.

Answered: Find a polynomial of degree 3 (here ao,…

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.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section4.2: Complex Solutions Of Equations

Problem 7ECP: Find the cubic polynomial function f with real coefficients that has 1 and 2+i as zeros, and f2=2.

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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.

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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