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Math Help - Finding x's of a 4th degree.

  1. #1
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    Finding x's of a 4th degree.

    I've tried factoring as best as I can, I've tried to apply what little I can understand about the rational roots theorem. I've tried grouping. All to no avail. I think it must be a tricky one.

    Function is.
    <br />
f(x)=x^4+8x^3+6x^2-18x-10<br />
    Thoughts? Any obvious giveaways I'm overlooking? Root at
     \sqrt{2}

     \sqrt{-2}?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    If you want I can give you answer in decimals without solution( from calculator) but that will not be the ideal way to approach it, do you want it?
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  3. #3
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    Factoring won't work because this equation has no rational roots. And it is easy to see, by putting them into the equation, that neither \sqrt{2} nor i\sqrt{2} is a solution.

    You will have to resort to numerical solution, as ADARSH suggests, or the "quartic formula" which is very complicated: see
    Solving Quartic Equations
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    I think that wont be a very difficult method after sufficient practice , any other methods?
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