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Math Help - Solving 4th order polynomial equations

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    Solving 4th order polynomial equations

    How do you solve for x with a fourth order polynomial?

    The problem I'm working with now is asking for the largest possible value of x for the equation 8x^4 - 16x^2 = 4.


    I've played around with it some, but can't work out a viable way to solve for x. Any suggestions are appreciated.
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    Re: Solving 4th order polynomial equations

    Have you considered the Quadratic nature of this particular example? If you don't see it, substitute y = x^2 and it should become obvious.
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    Re: Solving 4th order polynomial equations

    Quote Originally Posted by TKHunny View Post
    Have you considered the Quadratic nature of this particular example? If you don't see it, substitute y = x^2 and it should become obvious.
    Hmmm...I'm afraid I don't follow. I factored and tried to adopt it into quadratic form, but it didn't work out. The substitution didn't really open it up for me, but I'm sure I'm missing something simple...
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    Re: Solving 4th order polynomial equations

    May as well start by cancelling 4: 2x^4 - 4x^2 -1 =0

    This is equal to 2(x^2)^2 - 4(x^2) -1 =0. Taking TKHunny's suggestion and saying that y=x^2 then it becomes 2y^2-4y-1=0. That is standard quadratic form which can be solved using your favourite method.

    Once you have solutions for y take the square root to get your x values.


    edit: This equation doesn't factor, use the quadratic formula or complete the square

    edit 2: You'll get four solutions although some may be complex
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    Re: Solving 4th order polynomial equations

    Thanks guys, it worked out well.

    I appreciate the help!
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