Explanation Given: A polynomial function p ( x ) = a 0 + a 1 x + a 2 x 2 Proof: Considering the polynomial function p ( x ) = a 0 + a 1 x + a 2 x 2 . The values that x takes are x = − 1 , 0 , 1. Substituting x = − 1 in p ( x ). p ( x ) = a 0 + a 1 ( − 1 ) + a 2 ( − 1 ) 2 = a 0 − a 1 + a 2 Substituting x = 0 in p ( x ). p ( x ) = a 0 + a 1 ( 0 ) + a 2 ( 0 ) 2 = a 0 Substituting x = 1 in p ( x ). p ( x ) = a 0 + a 1 ( 1 ) + a 2 ( 1 ) 2 = a 0 + a 1 + a 2 Set p ( x ) = 0 in each of the above equation, a 0 − a 1 + a 2 = 0 a 0 = 0 a 0 + a 1 + a 2 = 0 Writing this system in augmented matrix [ 1 − 1 1 0 1 0 0 0 1 1 1 0 ] By using Gauss elimination method to solve the system

Elementary Linear Algebra - Text Only (Looseleaf)

8th Edition

ISBN: 9781305953208

Author: Larson

Publisher: Cengage Learning

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Chapter 1.3, Problem 39E

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To prove:

If a polynomial function p(x)=a0+a1x+a2x2 is zero for x=−1,x=0,and x=1, then a0=a1=a2=0.

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Chapter 1.3, Problem 38E

Chapter 1.3, Problem 40E

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Elementary Linear Algebra - Text Only (Looseleaf)

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To prove: If a polynomial function p ( x ) = a 0 + a 1 x + a 2 x 2 is zero for x = − 1 , x = 0 , and x = 1 , then a 0 = a 1 = a 2 = 0 .

Solution Summary: The author explains that if a polynomial function p(x)=a_0+

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To prove:

If a polynomial function p(x)=a0+a1x+a2x2 is zero for x=−1,x=0,and x=1, then a0=a1=a2=0.

Want to see the full answer?

Chapter 1 Solutions

To prove: If a polynomial function p ( x ) = a 0 + a 1 x + a 2 x 2 is zero for x = − 1 , x = 0 , and x = 1 , then a 0 = a 1 = a 2 = 0 .

Solution Summary: The author explains that if a polynomial function p(x)=a_0+

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To prove: If a polynomial function p(x)=a0+a1x+a2x2 is zero for x=−1,x=0,and x=1, then a0=a1=a2=0.

Want to see the full answer?

Chapter 1 Solutions

To prove:

If a polynomial function p(x)=a0+a1x+a2x2 is zero for x=−1,x=0,and x=1, then a0=a1=a2=0.