6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r* - 4x+ 3 + 14 + 26. Hint. There is a mathematical statement that says if p (r) is a polynomial with real coeffi- cients and a + bi is a complex root of p (#), then a – bi is also a root of p (x). If, respoctively, 1- 2i and 3 + 2i are roots of the polynomials a) and b) given above, then applying the statement will give a second root. Find the other roots. Do not use any caleulating devices to find the other roots. Show your work for finding the other roots.
6. Find all the roots of the following polynomials: a) p(r) = * - 3.r" +?+ 7x – 30 and b) p (r) = r* - 4x+ 3 + 14 + 26. Hint. There is a mathematical statement that says if p (r) is a polynomial with real coeffi- cients and a + bi is a complex root of p (#), then a – bi is also a root of p (x). If, respoctively, 1- 2i and 3 + 2i are roots of the polynomials a) and b) given above, then applying the statement will give a second root. Find the other roots. Do not use any caleulating devices to find the other roots. Show your work for finding the other roots.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:6. Find all the roots of the following polynomials:
a) p(r) = a* – 3.r +x² + 7x – 30
and
b) p (r) = r* - 4.r + 3² + 14:r + 26.
Hint. There is a mathematical statement that says if p (r) is a polynomial with real coeffi-
cients and a + bi is a complex root of p (x), then a – bi is also a root of p (r). If, respectively,
1- 2i and 3+ 2i are roots of the polynomials a) and b) given above, then applying the
statement will give a second root. Find the other roots. Do not use any caleulating devices
to find the other roots. Show your work for finding the other roots.
1
Bonus: Let A = {-3, –2, –1,0, 1,2,3} and B = {-10, –9, ...,9, 10} be sets. A function
f: A - B is defined by
f (n) = {
n2, if ne{-1,0,1)
-n, if ne{-2,2}
n2-9, if ne(-3,3)
a) Write the function f (n) as a set of ordered pairs.
b) What is the domain, codomain, and range of the function?
c) What is f (X) where X = {-3, –2, –1}?
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