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Math Help - [SOLVED] Miscellaneous 6 OCR

  1. #1
    james singh jagjit
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    Unhappy [SOLVED] Miscellaneous 6 OCR

    Hi everyone, I am new in this forum. Anyway I have been struggling with an inequality question in my homework, unfortunately due in tomarrow.

    Find the value of k for the following equation which has 2 real roots

    Kx^2 + kx + 2 = 0

    Now I have found that: b^2 -4ac
    k^2 - 4*k*2> 0
    K^2 -8k > 0

    I do not understand what to do after this stage because it is not possible to expand the brackets or square root the 8
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by james singh jagjit View Post
    Hi everyone, I am new in this forum. Anyway I have been struggling with an inequality question in my homework, unfortunately due in tomarrow.

    Find the value of k for the following equation which has 2 real roots

    Kx^2 + kx + 2 = 0

    Now I have found that: b^2 -4ac
    k^2 - 4*k*2> 0
    K^2 -8k > 0

    I do not understand what to do after this stage because it is not possible to expand the brackets or square root the 8
    b^2 - 4ac > 0

    k^2 - 4(k)(2) > 0

    k( k - 8 ) > 0

    Thus

    ---0_________8---


     k < 0 \ and \ 8 < k


    ---
    Thanks for the spot Jhevon!
    Last edited by janvdl; November 26th 2007 at 09:01 AM. Reason: Stupid mistake
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  3. #3
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    Hello, James!

    Welcome aboard!


    Find the value of k for which the following equation
    has two real roots: . kx^2 + kx + 2 \:= \:0

    Now I have found that: . b^2 -4ac \:> \;0

    So we have: . k^2 -8k \:> \:0
    Factor: . k(k-8) \:>\:0

    It says: The product of two numbers is positive.
    When does this happen?
    . . It happens in two ways . . .

    [1] Both factors are positive: . \begin{Bmatrix}k & > & 0 & \Rightarrow & k & > & 0 \\ k - 8 & > & 0 & \Rightarrow & k & > & 8 \end{Bmatrix}\quad\Rightarrow\quad k \:> \:8

    [2] Both factors are negative: . \begin{Bmatrix}k & < & 0 & \Rightarrow & k & < & 0 \\ k-8 & <&  0 & \Rightarrow & k &<& 8 \end{Bmatrix}\quad\Rightarrow\quad k \:<\:0


    Therefore, the equation has two real roots for: .  k\,\in\,(-\infty,0) \cup (8,\infty)
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