Results 1 to 6 of 6

Math Help - complex no. question no. 8

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    176

    complex no. question no. 8

    p307 q10
    prove that
    x^5 -1 = (x-1)(x^2-2x cos \frac {2\pi}{5} +1)(x^2-2xcos\frac{4\pi}5+1)
    would anyone just give me some hints on this type of question? thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,855
    Thanks
    321
    Awards
    1
    Quote Originally Posted by afeasfaerw23231233 View Post
    p307 q10
    prove that
    x^5 -1 = (x-1)(x^2-2x cos \frac {2\pi}{5} +1)(x^2-2xcos\frac{4\pi}5+1)
    would anyone just give me some hints on this type of question? thanks.
    You mean aside from it not being true?

    x^5 - 1 = (x - 1)(x^4 + x^2 + 1)

    I assume since the title of the post involves complex numbers that you left two i's out of this. (The kid is crying so I don't have time to figure out where. )

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Quote Originally Posted by topsquark View Post
    You mean aside from it not being true?

    x^5 - 1 = (x - 1)(x^4 +{\color{red}x^3}+ x^2+{\color{red}x} + 1)

    I assume since the title of the post involves complex numbers that you left two i's out of this. (The kid is crying so I don't have time to figure out where. )

    -Dan



    (good luck with your boy )
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    Quote Originally Posted by afeasfaerw23231233 View Post
    p307 q10
    prove that
    x^5 -1 = (x-1)(x^2-2x cos \frac {2\pi}{5} +1)(x^2-2xcos\frac{4\pi}5+1)
    would anyone just give me some hints on this type of question? thanks.
    x^5-1=(x-1)(1+x+x^2+x^3+x^4)

    A polynomial of degree 4 is necessarily a product of two polynomials of degree 2.

    Why ?
    This has to do with the d'Alembert-Gauss theorem, which states that any polynomial can be developped into a product of polynomial of degree 1 containing complex numbers.
    However, I don't know (or don't remember I've learnt it..) why a polynomial can always be a product of polynomials of degree 1 or 2...


    Getting back to the problem :

    x^4+x^3+x^2+x+1=(x^2+ax+b)(x^2+cx+d)

    Develop in order to find a, b, c and d...

    Edit : it seems that the first attempts are vain for solving..
    Last edited by Moo; May 22nd 2008 at 11:56 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by afeasfaerw23231233 View Post
    p307 q10
    prove that
    x^5 -1 = (x-1)(x^2-2x cos \frac {2\pi}{5} +1)(x^2-2xcos\frac{4\pi}5+1)
    would anyone just give me some hints on this type of question? thanks.
    The attachment I gave at this thread: http://www.mathhelpforum.com/math-he...-hard-way.html

    might be of indirect interest to you.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,855
    Thanks
    321
    Awards
    1
    Quote Originally Posted by topsquark View Post
    You mean aside from it not being true?

    x^5 - 1 = (x - 1)(x^4 + + x^3 + x^2 + x + 1)

    I assume since the title of the post involves complex numbers that you left two i's out of this. (The kid is crying so I don't have time to figure out where. )

    -Dan
    Like I said!

    Okay, I goofed. Thanks for the catch, Moo.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 4th 2011, 05:30 AM
  2. complex question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 25th 2011, 04:38 PM
  3. Complex No.s Question (arg)
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: April 7th 2010, 03:43 AM
  4. complex no. question no. 7
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 21st 2008, 11:44 AM
  5. complex no. question no. 6
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 21st 2008, 01:20 AM

Search Tags


/mathhelpforum @mathhelpforum