Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Prove It

Math Help - Factoring 5th root polynomial

  1. #1
    Junior Member froodles01's Avatar
    Joined
    Nov 2011
    From
    Surrey UK
    Posts
    49
    Thanks
    1

    Post Factoring 5th root polynomial

    My question started with
    Show -243 in polar form which I did, <243, ∏ >
    Then find all fifth roots of -243, which I did
    z0 = <3, ∏/5 >
    z1
    . . . .
    z4 = <3, 9∏/5 >

    Now I need to factorise the polynomial z^5 + 243 giving exact values of the real coeff's. in terms of sin, cos where appropriate.

    I think it should be simple for me, but need a quick start as to what is being looked for.

    Thank you for looking.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,653
    Thanks
    1478

    Re: Factoring 5th root polynomial

    Quote Originally Posted by froodles01 View Post
    My question started with
    Show -243 in polar form which I did, <243, ∏ >
    Then find all fifth roots of -243, which I did
    z0 = <3, ∏/5 >
    z1
    . . . .
    z4 = <3, 9∏/5 >

    Now I need to factorise the polynomial z^5 + 243 giving exact values of the real coeff's. in terms of sin, cos where appropriate.

    I think it should be simple for me, but need a quick start as to what is being looked for.

    Thank you for looking.
    Well you already have all the fifth roots, though the arguments should be in the region \displaystyle \begin{align*} \theta \in (-\pi, \pi] \end{align*}.

    So the factorisation of \displaystyle \begin{align*} z^5 + 243 \end{align*} will be \displaystyle \begin{align*} (z - z_1)(z - z_2)(z - z_3)(z - z_4)(z - z_5) \end{align*}.
    Thanks from froodles01
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factoring given a root
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: August 22nd 2011, 12:57 PM
  2. Polynomial factoring help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 17th 2009, 09:07 AM
  3. Factoring a polynomial
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 11th 2008, 03:34 AM
  4. polynomial factoring
    Posted in the Algebra Forum
    Replies: 7
    Last Post: January 14th 2008, 12:28 PM
  5. polynomial root
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 19th 2006, 10:31 AM

Search Tags


/mathhelpforum @mathhelpforum