Assignment 5 Solutions

Assignment 5 Solutions - Assignment 5 1. What polynomial...

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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=x-1.- 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....
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This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Fall '10 term at Carleton.

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Assignment 5 Solutions - Assignment 5 1. What polynomial...

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