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Math Help - roots of equations

  1. #1
    abz
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    roots of equations

    Determine the roots of the equation
    x2 – 3x – 8 = 0
    Last edited by CaptainBlack; July 10th 2008 at 11:11 PM.
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  2. #2
    Moo
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    Hello,

    Quote Originally Posted by abz View Post
    Determine the roots of the equation
    x2 – 3x – 8 = 0
    x^2-3x-8=0

    Discriminant method :
    \Delta=9+32=41

    --> x=\frac{3 \pm \sqrt{41}}{2}

    Completing the square method :
    x^2-3x-8=x^2-2 \cdot {\color{red}\frac 32} x-8=\left(x-\frac 32 \right)^2-\left(\frac 32\right)^2-8=\left(x-\frac 32 \right)^2-\frac 94-8

    =\left(x-\frac 32 \right)^2-\frac{41}{4}=\left(x-\frac 32 \right)^2-\left(\frac{\sqrt{41}}{2}\right)^2

    Difference of 2 squares : a^2-b^2=(a-b)(a+b)

    ---> x^2-3x-8=\left(x-\frac 32+\frac{\sqrt{41}}{2}\right)\left(x-\frac 32-\frac{\sqrt{41}}{2}\right)

    Therefore, x-\frac 32+\frac{\sqrt{41}}{2}=0 or x-\frac 32-\frac{\sqrt{41}}{2}=0
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