H2 Maths Question

LastRide7 SG

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.

wee_ws SG

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

LastRide7 SG

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?

wee_ws SG

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