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Thread: Find a and m in this equation: x^2+2(m-a)x+3am-2=0

  1. #1
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    Find a and m in this equation: x^2+2(m-a)x+3am-2=0

    There is the following equation:
    x^2+2(m-a)x+3am-2=0 | a,m ∈ R
    a) Find a such that the euation has real roots, ∀ m ∈ R.
    b) Find m such that the euation has real roots, ∀ a ∈ R.
    I put the condition: DELTA >= 0
    I found DELTA but since this step I have problems..
    Sorry for my english!
    The answer should be: |a| <= sqrt(8/21) ; |m| <= sqrt(8/21)
    My try:

    Attached Images Attached Images

  2. #2
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    idea

    Can anyone give me a little help or an idea?

  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by Vali View Post
    There is the following equation:
    x^2+2(m-a)x+3am-2=0 | a,m ∈ R
    a) Find a such that the equation has real roots, ∀ m ∈ R.
    b) Find m such that the equation has real roots, ∀ a ∈ R.
    I put the condition: DELTA >= 0

    For what does "DELTA" stand? How does it relate to the posted question?

    Quote Originally Posted by Vali View Post
    I found DELTA but since this step I have problems.
    What were your steps? What did you obtain? How did this relate to "a" and "m"?

    Quote Originally Posted by Vali View Post
    The answer should be: |a| <= sqrt(8/21) ; |m| <= sqrt(8/21)
    My try:

    The image in the attachment appears to show the following:



    [tex]\Delta\, =\, h\, (a^2\, -\, 5am\, +\, m^2\, +\, 2)[/tex]

    [tex]a^2\, -\, 5am\, +\, m^2\, +\, 2\, \geq\, 0[/tex]

    [tex]\Delta '\, \geq\, 0[/tex]

    [tex]\Delta '\, =\, 25m^2\, -\, 3m^2\, -\, 8\, =\, )[/tex]

    [tex]\Delta '\, =\, 21m^2\, -\, 8[/tex]

    [tex]21m^2\, -\, 8\, \geq\, 0[/tex]

    [tex]21m^2\, \geq\, 8\, =\, )[/tex]

    [tex]\big|m\big|\, \geq\, \sqrt{\dfrac{8}{21}\,}[/tex]



    Please reply with confirmation or corrections, along with a clear explanation of what you're doing. Thank you!

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