Roots of a squared polynomial ( complex numbers)

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Homework Help Overview

The discussion revolves around finding the roots of a squared polynomial involving complex numbers. Participants are addressing the specific roots of the polynomial and the implications of squaring the variable.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the requirement to find all square roots of specific complex numbers and question the necessity of this step. There is confusion regarding the relationship between the polynomial and its squared form.

Discussion Status

The discussion is active with participants exploring different interpretations of the problem. Some guidance has been offered regarding the nature of the polynomial and its factors, but there is no explicit consensus on the approach to take.

Contextual Notes

Participants express uncertainty about the marking scheme and the expectations for solving the problem, indicating potential constraints in understanding the requirements.

Axe199
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Homework Statement



problem in a pic attached

Homework Equations





The Attempt at a Solution


i solved i and ii a , when it came to b , i just said that every one of the 3 roots will be squared having 2 roots 1 + and 1 - but then i read the marking schemes ( also attached) , and i got really confused and now i don't know what he wants from me
 

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Axe199 said:

Homework Statement



problem in a pic attached

Homework Equations





The Attempt at a Solution


i solved i and ii a , when it came to b , i just said that every one of the 3 roots will be squared having 2 roots 1 + and 1 - but then i read the marking schemes ( also attached) , and i got really confused and now i don't know what he wants from me

He wants you to tell him what are all the square roots of -2, -2+2*sqrt(3)*i and -2 - 2*sqrt(3)*i.
 
Ray Vickson said:
He wants you to tell him what are all the square roots of -2, -2+2*sqrt(3)*i and -2 - 2*sqrt(3)*i.

why can't i just say (z+2)^2= 0 and solve and do the same for the complex roots?
why do i have to find the roots of the -2?
 
Axe199 said:
why can't i just say (z+2)^2= 0 and solve and do the same for the complex roots?
why do i have to find the roots of the -2?

(z + 2)2 is not a factor of p(z2). It is a factor of (p(z))2, however, a completely different polynomial.
The polynomial is not the object being squared. p(z2) only means that the variable z is being replaced with the variable z2. So, as a result, we know that z2 + 2 is a factor.
 
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slider142 said:
(z + 2)2 is not a factor of p(z2). It is a factor of (p(z))2, however, a completely different polynomial.
The polynomial is not the object being squared. p(z2) only means that the variable z is being replaced with the variable z2. So, as a result, we know that z2 + 2 is a factor.
okay...thanks very much, tht was a tricky one, or maybe i am stupid :D
either way , thanks , i got it
 

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