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Math Help - find out the equation with the roots given

  1. #1
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    find out the equation with the roots given

    i need to find out the equation, the roots are given:

    -1+2√2 and -1-2√2
    2 2


    pls help
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Ilsa View Post
    i need to find out the equation, the roots are given:

    -1+2√2 and -1-2√2
    2 2


    pls help
    [x - (\frac{-1+2\sqrt2}{2})] \times [x - (\frac{-1-2\sqrt2}{2})]
    Last edited by e^(i*pi); September 26th 2009 at 06:58 AM.
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  3. #3
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    you can also use this formula

    x^2 - (sum of roots) x + (product of roots ) = 0
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  4. #4
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    x^2 + x + C = 0

    x = [-1 +- sqrt(1 - 4C)] / 2

    Get my drift?
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  5. #5
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    Exclamation

    i am using the formula bu can't get the equation, pls help by giving complete steps ~ thankyou.
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  6. #6
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    Talking

    Quote Originally Posted by Ilsa View Post
    i am using the formula bu can't get the equation
    Where are you stuck in the multiplication process?

    Please be complete. Thank you!
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  7. #7
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    x^2-(sum \ of\ roots)x+product \ of \ roots=0
     \\ \alpha= \frac{-1+2\sqrt{2}}{2}\ \ \beta= \frac{-1-2\sqrt{2}}{2}
     \alpha+ \beta= \frac{-1+2\sqrt{2}}{2}\ +\frac{-1-2\sqrt{2}}{2}\ = \frac{-1}{2}+\frac{2\sqrt{2}}{2}\ +\frac{-1}{2}-\frac{2\sqrt{2}}{2}
     \alpha+ \beta=\frac{-2}{2} =\ -1
     \\ \alpha \beta= \{ \frac{-1+2\sqrt{2}}{2}\ \} \{ \frac{-1-2\sqrt{2}}{2} \} \ = \{ \frac{1-2\sqrt{2}}{2}\ \} \{ \frac{1+2\sqrt{2}}{2} \}
    \\ \alpha \beta=\frac {\{1^2-(2\sqrt{2})^2\}}{4} \ = \frac{(1-8)}{4}=\frac{-7}{4}
    therefore ,the equation is
    \\ x^2-(\alpha +\beta)x+\alpha. \beta=0
    \\ x^2-(-1)x+\frac{-7}{4}=0
    \\ 4x^2+4x-7=0
    Last edited by ramiee2010; September 28th 2009 at 09:38 AM. Reason: print solution using latex
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