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)

Quote:

Originally Posted by Mr_Green

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

Quote:

Originally Posted by Mr_Green

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