This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Assignment 5 1. What polynomial has roots which are reciprocals of: x 4 + 2 x 3 + 2 x 2 10 x 20. To get reciprocals of roots, simply switch the order of coecients: 20 x 4 10 x 3 + 2 x 2 + 2 x + 1 2. What polynomial has roots which three times those of 3 x 4 + 2 x 3 x 2 + 4 x 5. Simply sub in x 3 for x.(then find the common denominator and factor it out. 3 ( x 3 ) 4 + 2 ( x 3 ) 3 ( x 3 ) 2 + 4 ( x 3 ) 5 3 ( x 4 3 4 ) + 2 ( x 3 3 3 ) ( x 2 3 2 ) + 4 ( x 3 ) 5 1(3 x 4 ) + 3(2 x 3 ) + 3 2 ( x 2 ) + 3 3 (4 x ) + 3 4 ( 5) 81 3 x 4 + 6 x 3 9 x 2 + 108 x 405 81 3 x 4 + 6 x 3 9 x 2 + 108 x 405 3. What polynomial has roots are 1 larger that those of x 4 4 x 3 +14 x 2 + 2 x 1. Use repeated synthetic division to get the polynomial for x=x1. 1 1 1 1 1 1 4 14 2 1 1 3 17 15 1 3 17 15 14 1 2 19 1 2 19 34 1 1 1 1 20 1 1  1 So the polynomial we want is x 4 + 20 x 2 34 x + 14....
View
Full
Document
This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Fall '10 term at Carleton.
 Fall '10
 Unknown
 Linear Algebra, Algebra

Click to edit the document details