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Thread: equation 1

  1. #1
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    equation 1

    $\displaystyle

    \begin{array}{l}
    solve\;in\;R \\
    \\
    x^4 - 2x^2 - 400x = 9999 \\
    \end{array}

    $
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  2. #2
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    Bring everything to one side

    $\displaystyle x^4 - 2x^2 - 400x - 9999 = 0$.

    Now work out the factors (positive and negative) of $\displaystyle 9999$.

    Substitute each of these factors into the polynomial.

    By the factor theorem, if any of these factors (call it $\displaystyle a$) makes the polynomial $\displaystyle = 0$, then $\displaystyle x - a$ is a factor.
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  3. #3
    MHF Contributor Unknown008's Avatar
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    Solve in R? Do you mean for the real solutions?

    Anyway, rearrange;

    $\displaystyle x^4 - 2x^2 - 400x - 9999= 0$

    Then, I'll use the factor theorem.

    Let f(x) = x^4 - 2x^2 - 400x - 9999

    By trial and error, find the values of x that are factors of 9999 that make f(x) = 0. Those are the factors of your equation.

    Use long division or inspection to divide f(x) by their factors to get other factors, until you get a quadratic which is more easily factorised.

    If it cannot be solved, then the values you got for f(x) = 0 are the only solutions.

    EDIT: Woops, too late... I was making sure there were solutions =S
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