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Quadratic function problem

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data

    ..........................49ac-12b2
    (4α-3β)(3α-4β) =------------------------
    ....................................a2

    Deduce that, If 12b2< 49ac< 49b2/2

    then β lies between 3α/4 and 4α/3

    2. Relevant equations

    α+β = -b/a

    αβ = c/a

    3. The attempt at a solution
     
    Last edited: Sep 17, 2010
  2. jcsd
  3. Sep 17, 2010 #2
    I don't know how to do this.

    I have even a idea to about these type of question, please help me
     
  4. Sep 17, 2010 #3

    Mentallic

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    Well, start by expanding the left hand side of that equality. Use the related equations you've given and remember the fact that [tex](a+b)^2=a^2+b^2+2ab[/tex]
     
  5. Sep 17, 2010 #4
    12α2-25αβ + 12β2

    Using this i got that this in terms of a, b & c.

    Next part of the question is this. How should i do it
     
  6. Sep 18, 2010 #5

    Mentallic

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    Right so looking at your a2 and b2 part, if [tex](a+b)^2=a^2+b^2+2ab[/tex] then [tex]a^2+b^2=(a+b)^2-2ab[/tex]
     
  7. Sep 21, 2010 #6
    12α2 + 12β2 = (12α+12β)2 - 313αβ
     
    Last edited: Sep 21, 2010
  8. Sep 22, 2010 #7

    Mentallic

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    No not quite. If you expanded that you would get [tex](12a)^2+(12b)^2=144a^2+144b^2[/tex]

    [tex]12a^2+12b^2=12(a^2+b^2)=12((a+b)^2-2ab)[/tex]

    Now go on from this.
     
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