d. By experiment, guess or derivation, find real numbers r and s so that An+2 + ran+1+ san = 0, bn+2+rbn+1+ sb, = 0 %3D and prove the relation. What is the connection between 3+ i and the polynomial X² + rX + s? Hint: there is nothing particularly special about 3+i.
d. By experiment, guess or derivation, find real numbers r and s so that An+2 + ran+1+ san = 0, bn+2+rbn+1+ sb, = 0 %3D and prove the relation. What is the connection between 3+ i and the polynomial X² + rX + s? Hint: there is nothing particularly special about 3+i.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 52E
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Let (3+i)^n=a_n +ib_n.
I found the r and s values to be -6 and 10. I just don't know how to answer the connection between 3+i and the polynomial X^2+rX+s. There needs to be a more general type of answer other than 3+i is one of the roots of the polynomial.
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