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Maths - a proof question on the nature of roots of quadratic equations

  1. Apr 14, 2012 #1
    I'm sorry, I just realised I put this in the wrong subsection. While I figure out how to fix that, please have a look anyway.
    __

    1. The problem statement, all variables and given/known data

    Given x [itex]\inℝ[/itex]
    And s =[itex]\frac{4(x^{2}) + 3}{2x-1}[/itex]
    Prove that [itex]s^{2}[/itex] -4s - 12 ≥ 0

    2. Relevant equations
    The discriminant Δ, (in order for which to be real must be ≥ 0)
    b^2 - 4ac ≥ 0

    3. The attempt at a solution
    Doing the algebra isn't the problem, I'm having trouble understanding the question itself. For this sort of proof, don't I need to work with
    s =[itex]\frac{4(x^{2}) + 3}{2x-1}[/itex]
    instead of the statement to be proven, which is [itex]s^{2}[/itex] -4s - 12 ≥ 0?

    In which case, how do I apply the b^2 - 4ac rule with the linear equation part in the denominator?
     
    Last edited: Apr 14, 2012
  2. jcsd
  3. Apr 15, 2012 #2
    The variable is ##x##, so make the given equation look like a regular quadratic in ##x##. Then pick off what ##a##, ##b##, and ##c## are and write the inequality for ##\Delta## in terms of those. It will quickly resolve into what's requested.
     
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