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Math Help - finding undefined values

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    finding undefined values

    Determine all values of x for which f is not defined.

    f(x) = (2x^3 + 5x^2 -22x + 15) / (2x^3 + 15x^2 - 34x + 24)
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mr_Green View Post
    Determine all values of x for which f is not defined.

    f(x) = (2x^3 + 5x^2 -22x + 15) / (2x^3 + 15x^2 - 34x + 24)
    Hint: a rational function is undefined wherever its denominator is zero
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mr_Green View Post
    Determine all values of x for which f is not defined.

    f(x) = (2x^3 + 5x^2 -22x + 15) / (2x^3 + 15x^2 - 34x + 24)
    Is there a typo here? I'm not getting a nice answer here...

    You need to find where the denominator is zero, so the problem becomes how do you find the zeros of
    2x^3 + 15x^2 - 34x + 24

    Well, all rational zeros of this polynomial have the form
    \frac{\text{factors of }24}{\text{factors of }2}

    So your list of possible rational zeros is
    \pm(\frac{1}{2}, 1, 2, 3, 4, 6, 8, 12, 24)

    Since none of these work you need to resort to something like Cardano's method (very ugly) or numerical approximation. I get that there is one real zero around -9.44.

    -Dan
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