Results 1 to 9 of 9
Like Tree3Thanks
  • 1 Post By HallsofIvy
  • 2 Post By greg1313

Thread: power of 5 and above

  1. #1
    Newbie
    Joined
    Jun 2018
    From
    Dimona
    Posts
    15

    power of 5 and above

    Why equations with power of 5 and above don't have a way to slove them?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,929
    Thanks
    359

    Re: power of 5 and above

    x^5 = 32
    x = ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,926
    Thanks
    3098

    Re: power of 5 and above

    If you mean "why do polynomial equations of degree 5 and higher not have a general method that applies to all such equations" it was proved that there exist such polynomials that have solutions that cannot be written in terms of roots.

    See the "Abel-Ruffini theorem": https://en.wikipedia.org/wiki/Abel%E...uffini_theorem
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,929
    Thanks
    359

    Re: power of 5 and above

    thinking out loud:
    if (x-a)(x-b)(x-c)(x-d)(x-e) = 0
    then at least one of a,b,c,d,e = x

    Halls, should I say: stinking out loud?!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,926
    Thanks
    3098

    Re: power of 5 and above

    Whatever turns you on.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jun 2018
    From
    Dimona
    Posts
    15

    Re: power of 5 and above

    Quote Originally Posted by DenisB View Post
    thinking out loud:
    if (x-a)(x-b)(x-c)(x-d)(x-e) = 0
    then at least one of a,b,c,d,e = x

    Halls, should I say: stinking out loud?!
    (1)How I know that:
    (a - x)(b - x)...(z - x)
    have a power greater than 3?
    (2)Why the equation is polynomial equation?
    (3)How I know that equation that write (not like in (1) question) is polynomial that isn't seen polynomial at first sight?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Feb 2015
    From
    Ottawa Ontario
    Posts
    1,929
    Thanks
    359

    Re: power of 5 and above

    Please have someone help you with your English,
    and post in proper English...else we can't help...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Nov 2010
    Posts
    3,631
    Thanks
    1457

    Re: power of 5 and above

    Quote Originally Posted by yyakob View Post
    (1)How I know that:
    (a - x)(b - x)...(z - x)
    have a power greater than 3?
    (2)Why the equation is polynomial equation?
    (3)How I know that equation that write (not like in (1) question) is polynomial that isn't seen polynomial at first sight?
    (1) and (3): Multiply it out:

    $$(x-a)(x-b)(x-c)(x-d)(x-e) = x^5-(a+b+c+d+e)x^4+(ab+ac+ad+ae+bc+bd+be+cd+ce+de)x^3-(abc+abd+abe+acd+ace+ade+bcd+bce+bde+cde)x^2+(abcd +abce+bcde)x-abcde$$

    (2) Any equation with a polynomial on one side of the equation and a constant (or another polynomial) on the other is called a polynomial equation by definition. There is no reason for it other than that is its definition.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Dec 2016
    From
    Earth
    Posts
    192
    Thanks
    86

    Re: power of 5 and above

    Quote Originally Posted by yyakob View Post
    (1)How I know that:
    (a - x)(b - x)...(z - x)
    Is this supposed to be a trick question!?

    (a - x)(b - x)...(z - x) =

    (a - x)(b - x)...(w - x)(x - x)(y - x)(z - x) =

    (a - x)(b - x)...(w - x)(0)(y - x)(z - x) =

    0
    Thanks from SlipEternal and HallsofIvy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Mar 24th 2017, 01:05 AM
  2. Replies: 4
    Last Post: Sep 28th 2014, 05:55 PM
  3. Replies: 1
    Last Post: Apr 12th 2014, 12:45 PM
  4. Exponents power to a power
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Feb 27th 2009, 12:39 AM
  5. Replies: 6
    Last Post: May 1st 2008, 01:21 PM

/mathhelpforum @mathhelpforum