Question 949294
I think you're looking for the roots and not the asymptotes here, because there are no asymptotes.
{{{graph(300,300,-5,5,-10,10,x^4 + 3x^3 - 5x^2 - 9x - 2 )}}}
Looks like {{{x=-1}}} and {{{x=2}}} are both roots. 
That greatly narrows the choices of answers down.
I would suggest plugging in each value into the equation to verify that they are indeed solutions.
Example:
{{{x=-1}}}
{{{y=(-1)^4+3(-1)^3-5(-1)^2-9(-1)-2=1-3-5+9-2=0}}}