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Math Help - Quadratic with fractions - completing the square or formula

  1. #1
    Junior Member froodles01's Avatar
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    Post Quadratic with fractions - completing the square or formula

    Doing past papers at the mo & have a quadratic which I am stuck on

    find fixed points of f(x) = x^2+(13/12)x-1/2
    Now, fixed points are when f(x) = x, so I have subtracted x from both sides

    => x^2 + (1/12)x - 1/2 = 0 to make an easier(?) quadratic
    so a=1, b=1/12 & c=-1/2

    Sub into formula & I am now stuck as the sqrt comes up as negative & I'm not sure enough about completing the square.


    I also have similar equation f(x) = x^2 + (14/15)x - 2/5. Stuck here, too

    Would appreciate a little help.
    Thank you
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    Member sbhatnagar's Avatar
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    Re: Quadratic with fractions - completing the square or formula

    x^2+\Big( {1 \over 12}\Big)x-\frac{1}{2}=0

    D=\Big( {1 \over 12}\Big)^2-4\Big( -\frac{1}{2}\Big)=\frac{1}{144}+2=\frac{289}{144} \quad(\text{... which is positive})

    You can also multiply both sides by 12 to get

    12x^2+x-6=0

    \implies x= \frac{-1 \pm \sqrt{1-4(-6)(12)}}{12(2)}
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    Junior Member froodles01's Avatar
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    Re: Quadratic with fractions - completing the square or formula

    Hi.
    I have the second example, too, which I have still not been able to do. Similar equation f(x) = x^2 + (14/15)x - 2/5
    Please could someone point me in the right direction with this, too. It is part of a fixed point iteration question.
    I'm having trouble with that, too, but I must keep trying.
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    Re: Quadratic with fractions - completing the square or formula

    Quote Originally Posted by froodles01 View Post
    Doing past papers at the mo & have a quadratic which I am stuck on

    find fixed points of f(x) = x^2+(13/12)x-1/2
    Now, fixed points are when f(x) = x, so I have subtracted x from both sides

    => x^2 + (1/12)x - 1/2 = 0 to make an easier(?) quadratic
    so a=1, b=1/12 & c=-1/2

    Sub into formula & I am now stuck as the sqrt comes up as negative & I'm not sure enough about completing the square.


    I also have similar equation f(x) = x^2 + (14/15)x - 2/5. Stuck here, too

    Would appreciate a little help.
    Thank you
    Are you trying to find the x intercepts for the second? If so...

    \displaystyle \begin{align*} x^2 + \frac{14}{15}x - \frac{2}{5} &= 0 \\ x^2 + \frac{14}{15} + \left(\frac{7}{15}\right)^2 - \left(\frac{7}{15}\right)^2 - \frac{2}{5} &= 0 \\ \left(x + \frac{7}{15}\right)^2 - \frac{49}{225} - \frac{90}{225} &= 0 \\ \left(x + \frac{7}{15}\right)^2 - \frac{139}{225} &= 0 \\ \left(x + \frac{7}{15}\right)^2 &= \frac{139}{225} \\ x + \frac{7}{15} &= \pm \frac{\sqrt{139}}{15} \\ x &= \frac{-7 \pm \sqrt{139}}{15} \end{align*}
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    Junior Member froodles01's Avatar
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    Re: Quadratic with fractions - completing the square or formula

    Oooh! Ideal. This DOES make my understanding better (as well as having the answer). I'll get there one day.
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