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Math Help - Finding real solutions

  1. #1
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    Finding real solutions

    For what values of c does the following equation have at least one real solution?

    cx^2+sqrt(c) x = c
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  2. #2
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    Re: Finding real solutions

    Quote Originally Posted by Saphira View Post
    For what values of c does the following equation have at least one real solution?
     cx^2+\sqrt{c}x=c
    You want (\sqrt{c})^2-4(c)(-c)\ge0
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  3. #3
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    Re: Finding real solutions

    Are we assuming c \ne 0?

    Are we assuming c \in \mathbb{R}?
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  4. #4
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    Re: Finding real solutions

    The value of c is not specified, so I'm guessing, yes.
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  5. #5
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    Re: Finding real solutions

    Quote Originally Posted by Plato View Post
    You want (\sqrt{c})^2-4(c)(-c)\ge0
    Thanks!
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  6. #6
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    Re: Finding real solutions

    Okay, have you considered the Quadratic Formula and the implications of the radical?
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  7. #7
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    Re: Finding real solutions

    Quote Originally Posted by Saphira View Post
    For what values of c does the following equation have at least one real solution?

    cx^2+sqrt(c) x = c
    1. c is positive since otherwise \sqrt{c} is not real and I presume we want it to be real.

    2. Rewrite the equation:

    cx^2+\sqrt{c}x-c=0

    What does Descartes rule of signs tell you when c>0.

    CB
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