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

See similar textbooks

Videos

Question

Chapter 1.3, Problem 39E

To determine

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.3, Problem 38E

Chapter 1.3, Problem 40E

Students have asked these similar questions

Practice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…

Answer the questions

How can I prepare for me Unit 3 test in algebra 1? I am in 9th grade.

Chapter 1 Solutions

Elementary Linear Algebra - Text Only (Looseleaf)

Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Linear Equations. In Exercises 1-6, determine...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...Ch. 1.1 - Parametric Representation. In Exercises 7-10, find...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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+

Videos

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+

Videos

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.