Prove, using an algebraic method, that (3x - 6) / x(x + 6) cannot lie between two certain values.
I know that the usage of discriminant is needed here but I don't know which one to use.
Hi,
This is a classical problem which should be covered in your school's lecture notes.
We usually start by letting y = (3x - 6) / {x(x + 6)}. Then we form a quadratic equation in x, since we want to consider the discriminant.
Thanks.
Cheers,
Wen Shih
Hi there, thank you for the help but I don't know whether to let the discriminant be greater than 0 or greater or equal to zero. Must we include the 0 in this case?
Hi,
It does not matter, what is important is that you are clear about what you are looking for.
If you consider discriminant >= 0, then you want to find the range of values of y (e.g., y <= a or y >= b) for which the curve lies in. So the required range for which the curve does not lie in will be a < y < b.
If you use discriminant < 0, then you want to find the set of values of y for which the curve does not lie in.
Thanks.
Cheers,
Wen Shih