# Hard discriminant question: values of k in (k+1)x^2-4kx+3k=0, number of solns

#### phillipa

##### New member Hi, I have the following problem and have little idea how to go about doing it:

For which values of k does (k+1)x^2-4kx+3k=0 have:
(i) one solution?
(ii) two solutions?
(iii) three solutions?

I know I need to find the discriminant then sub in to find 1, 2 and no solutions (I think?). I know how to do simple versions of these, but this just confuses me.
Attached a photo of my attempt at the first step (finding the discriminant) before subbing in to find 1, 2 and no solutions.

Thank you for any help.

#### Subhotosh Khan

##### Super Moderator
Staff member
View attachment 9192

Hi, I have the following problem and have little idea how to go about doing it:

For which values of k does (k+1)x^2-4kx+3k=0 have:
(i) one solution?
(ii) two solutions?
(iii) three solutions?

I know I need to find the discriminant then sub in to find 1, 2 and no solutions (I think?). I know how to do simple versions of these, but this just confuses me.
Attached a photo of my attempt at the first step (finding the discriminant) before subbing in to find 1, 2 and no solutions.

Thank you for any help.
If the equation was:

A * x^2 + B * x + C = 0 ..................(Where A, B & C are constant)

what would have been your discriminant?