305 -Homework set 6

This set is due April 3 at the beginning of lecture. Details of the homework policy can be found on the syllabus and here.

1. Find {\mathbb Q}^{p(x)} where p(x)=x^3-2, and determine all its subfields. Make sure you justify your answer. For example, if you state that two subfields {\mathbb F}_1 and {\mathbb F}_2 are different, you need to prove that this is indeed the case. 

2. Do the same for p(x)=x^4+x^3+x^2+x+1. 

[Updated, April 2: I guess the hint I gave for problem 2 makes no sense, sorry about that. Rather, you may want to begin by looking at how x^5-1 factors. Then, to compute \cos(72^\circ), it may be helpful to look at a triangle with angles \measuredangle 72^\circ, \measuredangle 72^\circ, and \measuredangle 36^\circ.]

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5 Responses to 305 -Homework set 6

  1. 305 -Syllabus « Teaching page says:
    March 21, 2009 at 10:42 am

    […] Homework 6, due April 3, at the beginning of lecture. Possibly related posts: (automatically generated)117b – Homework 5Buffalostyle Forges OnHomework battles and the biggest genius in the school, part IThe Myth About Homework […]

    Reply
  2. Tommy says:
    April 2, 2009 at 1:39 pm

    Concerning HW assignment 6, I am wondering if there is a typo in the hint you gave us for problem number 2. I may be wrong but I believe the denominator under the radical on the left hand side should be 18. Thanks!

    Reply
  3. andrescaicedo says:
    April 2, 2009 at 2:13 pm

    Hi Tommy,

    Hmm, yeah. I’m just about convinced now that the hint is nonsense. So, I have added another hint.

    Reply
  4. Karen says:
    April 2, 2009 at 8:10 pm

    Hi,
    Okay…I am struggling with the second problem. I have solved the quartic down to w^6 and found my value for w. Then, when I plug everything back in, I cannot get any given u to solve the equation where u^3 + ….=0. Therefore I am second guessing everything I have done. And I appreciate the new hint, but I’m not sure how to apply it. I have worked the equation many times, each time hoping my calculations are wrong…unfortunately so far, they are not.
    Any help would be greatly appreciated!

    Reply
  5. 305 -Syllabus | A kind of library says:
    February 17, 2019 at 6:34 am

    […] Homework 6, due April 3, at the beginning of lecture. […]

    Reply

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