Results 1 to 3 of 3
Like Tree2Thanks
  • 1 Post By johnsomeone
  • 1 Post By skeeter

Math Help - How do I find x with this polynomial function?

  1. #1
    Junior Member
    Joined
    Sep 2012
    From
    canada
    Posts
    28

    How do I find x with this polynomial function?

    How do I determine the values of x when f(x) = 48 when f(x) = x4 - 5x2 + 4. Please and thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    147

    Re: How do I find x with this polynomial function?

    Let w = x^2, then solve for w, then take square roots to find x values.

    Some polynomials are "secretly" solvable as quadratics. Here are some other eamples:

    4x^{20}-4x^{10}+1 = 0, \ q^8 + 7q^4 +6 = 0, \ z^{14}-z^7-56 = 0
    Thanks from misiaizeska
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,134
    Thanks
    1013

    Re: How do I find x with this polynomial function?

    x^4 - 5x^2 + 4 = 48

    x^4 - 5x^2 = 44

    complete the square ...

    x^4 - 5x^2 + \frac{25}{4} = 44 + \frac{25}{4}

    \left(x^2 - \frac{5}{2}\right)^2 = \frac{201}{4}

    x^2 - \frac{5}{2} = \pm \frac{\sqrt{201}}{2}

    assuming you're looking for real roots only ... x^2 > 0 for all x \ne 0

    x^2 = \frac{5 + \sqrt{201}}{2}

    x = \pm \sqrt{\frac{5 + \sqrt{201}}{2}}
    Thanks from misiaizeska
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: July 10th 2012, 06:46 AM
  2. Replies: 2
    Last Post: November 6th 2011, 12:30 AM
  3. Replies: 4
    Last Post: May 9th 2010, 02:46 PM
  4. Replies: 3
    Last Post: February 15th 2010, 06:40 PM
  5. Replies: 2
    Last Post: January 12th 2009, 08:44 AM

Search Tags


/mathhelpforum @mathhelpforum