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

  1. #1

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

    IMG_0485.jpg

    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.

  2. #2
    Elite Member
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    Quote Originally Posted by phillipa View Post
    IMG_0485.jpg

    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?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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