To me, your equation is a little ambiguous, and it could be interpreted in several ways. Can you try to be more clear? Is it like this:
The question goes like this:
Sketch the graph of y = 5 / x^2(x+3) , indicating clearly the equations of any asymptotes and turning points.
Hence, find the range of values of k if the number of real roots of the equation kx^2(x+3)=5 , where k is a constant is :
(i) three
(ii) one
The answer for the parts are (i) k>1.25
(ii) k<1.25,
How should i approach this question? and how can i find the asymptotes? thank you!!
So think about what makes an asymptote. It is when a function heads off toward infinity right? So see what happens when x becomes extremely large, or extremely small. Also, think of values of x that will make y extremely large or extremely small. That might give you a starting point. Hopefully you know how to find turning points by taking the derivative and looking for solutions giving 0 gradient.