Results 1 to 10 of 10

Math Help - How to convert these functions

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    18

    Red face How to convert these functions

    Hello there!

    In my work, I will have to convert functions. My English is crap, so I will just show you what I mean.

    If I have a function:

    y = x + 1 i can convert it to look like this: x = y - 1. I would like to do the same for:

    y = x^3 + x^2 + x + 1

    or this:

    y = x^4 + x^3 + x^2 + x + 1

    or this:

    y = x^5 + x^4 + x^3 + x^2 + x + 1

    How is that done?

    Thank you.

    Kind regards,
    Marius
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    For the first, you have this. For the second, you have this. For the third, in general, the quintic polynomial is not solvable (that's been proved, actually). Certain special cases can be solved, but not the general quintic.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2009
    Posts
    18
    Thank you!

    And what about this one?

    y = x^2 + x + 1

    Kind regards,
    Marius
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    That one's a quadratic. Rewrite as

    x^{2}+x+1-y=0, and use the quadratic formula to solve:

    x=\dfrac{-1\pm\sqrt{1-4(1-y)}}{2}=\dfrac{-1\pm\sqrt{4y-3}}{2}.

    Note that in order for everything to be real, you'd need 4y-3\ge 0, or y\ge 3/4.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2009
    Posts
    18
    Thanks for that!

    I found this one for the cubic:




    But couldnt find one for the quartic on wikipedia. Do you know what it looks like?

    Thanks! M
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Quote Originally Posted by king.oslo View Post
    Hello there!

    In my work, I will have to convert functions. My English is crap, so I will just show you what I mean.

    If I have a function:

    y = x + 1 i can convert it to look like this: x = y - 1. I would like to do the same for:

    y = x^3 + x^2 + x + 1
    This is a cubic.

    or this:

    y = x^4 + x^3 + x^2 + x + 1
    This is a quartic.

    or this:

    y = x^5 + x^4 + x^3 + x^2 + x + 1
    This is a quintic.

    How is that done?

    Thank you.

    Kind regards,
    Marius
    I don't know where you found your "cubic" formula, but it's not nearly complicated enough for a cubic. It looks like an incorrect quadratic. Here's the solution for your cubic. Here's the solution for your quartic.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2009
    Posts
    18
    Quote Originally Posted by Ackbeet View Post
    This is a cubic.



    This is a quartic.



    This is a quintic.



    I don't know where you found your "cubic" formula, but it's not nearly complicated enough for a cubic. It looks like an incorrect quadratic. Here's the solution for your cubic. Here's the solution for your quartic.
    Thanks! M
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You're welcome!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121
    A polynomial equation of degree 5 or higher cannot be solved in terms of radicals. There methods, using "special functions" for solving such equations.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Really? I didn't know that! Just doing a simple google search brought up the Jacobi theta function method, as well as hypergeometric functions (hypergeometric functions do seem to show up lots of different places, don't they? Maybe that's why the Russians do everything in terms of them.), as possibilities for solving the general quintic.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 30th 2011, 11:43 AM
  2. Does anyone know how to convert μW/m2 in μW/cm2 ?
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: March 10th 2011, 03:33 AM
  3. Does it convert or not?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 3rd 2011, 01:17 AM
  4. Convert in to m
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: September 3rd 2010, 04:44 PM
  5. convert km to mm
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: September 8th 2008, 03:32 PM

Search Tags


/mathhelpforum @mathhelpforum