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Math Help - Number and sign

  1. #1
    Super Member dhiab's Avatar
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    Number and sign

    m is the real parameter.
    Find the real number and sign for the equation :


    By two methods : graphic , algebric.
    Last edited by dhiab; July 24th 2009 at 11:56 AM.
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  2. #2
    J.R
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    solve the equation in \mathbb{C} perhaps ?

    x^2+6x+9m=0

    \delta=36(1-m)

    talk about the sign.

    for m>1 , m=1, m<1
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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by J.R View Post
    solve the equation in \mathbb{C} perhaps ?

    x^2+6x+9m=0

    \delta=36(1-m)

    talk about the sign.

    for m>1 , m=1, m<1
    Hello : Thank you this equation in R
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  4. #4
    J.R
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    so what happened when m<1 ?

    m=1 ?

    and m>1 ?
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  5. #5
    MHF Contributor red_dog's Avatar
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    Graphic.

    We have m=-\frac{1}{9}x^2-\frac{2}{3}x

    Intersect the graph of f(x)=-\frac{1}{9}x^2-\frac{2}{3}x with parallel lines to x-axis with equation y=m

    If m>1 then the line doesn't intersect the graph.

    If m=1 the line is tangent to the graph and the equation has a double solution x=-3

    If m\in(0,1) the line intersects the graph in 2 points and the equation has two negative solutions.

    If m=0 then the equation has the solutions x_1=-6, \ x_2=0

    If m<0 then the equation has one negative solution and one positive solution.
    Attached Thumbnails Attached Thumbnails Number and sign-graph.jpg  
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  6. #6
    Super Member dhiab's Avatar
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    Quote Originally Posted by red_dog View Post
    Graphic.

    We have m=-\frac{1}{9}x^2-\frac{2}{3}x

    Intersect the graph of f(x)=-\frac{1}{9}x^2-\frac{2}{3}x with parallel lines to x-axis with equation y=m

    If m>1 then the line doesn't intersect the graph.

    If m=1 the line is tangent to the graph and the equation has a double solution x=-3

    If m\in(0,1) the line intersects the graph in 2 points and the equation has two negative solutions.

    If m=0 then the equation has the solutions x_1=-6, \ x_2=0

    If m<0 then the equation has one negative solution and one positive solution.
    HELLO : ALGEBRIC SOLUTION
    Student sign of : delta , p=x1 x2 and s=x1 + x 2
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