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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- Aug 31st 2007, 03:04 AMMr_Greenfinding 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) - Aug 31st 2007, 03:38 AMJhevon
- Aug 31st 2007, 01:27 PMtopsquark
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

$\displaystyle 2x^3 + 15x^2 - 34x + 24$

Well, all rational zeros of this polynomial have the form

$\displaystyle \frac{\text{factors of }24}{\text{factors of }2}$

So your list of possible rational zeros is

$\displaystyle \pm(\frac{1}{2}, 1, 2, 3, 4, 6, 8, 12, 24)$

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