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

Thread: Factoring 5th root polynomial

  1. #1
    Junior Member froodles01's Avatar
    Joined
    Nov 2011
    From
    Surrey UK
    Posts
    51
    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
    12,880
    Thanks
    1946

    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 $\displaystyle \displaystyle \begin{align*} \theta \in (-\pi, \pi] \end{align*}$.

    So the factorisation of $\displaystyle \displaystyle \begin{align*} z^5 + 243 \end{align*}$ will be $\displaystyle \displaystyle \begin{align*} (z - z_1)(z - z_2)(z - z_3)(z - z_4)(z - z_5) \end{align*}$.
    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: Aug 22nd 2011, 12:57 PM
  2. Polynomial factoring help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jun 17th 2009, 09:07 AM
  3. Factoring a polynomial
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Oct 11th 2008, 03:34 AM
  4. polynomial factoring
    Posted in the Algebra Forum
    Replies: 7
    Last Post: Jan 14th 2008, 12:28 PM
  5. polynomial root
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Nov 19th 2006, 10:31 AM

Search Tags


/mathhelpforum @mathhelpforum