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Math Help - Real Roots

  1. #1
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    Real Roots

    If f(x) = x^3 - 6x^2 + p , where P is an arbitrary constant. For what values of p does f(x) have 3 distinct real roots?
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  2. #2
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    There is a general formula for the solution of a cubic, it is called Cardano's Formula. It would probably be a good place to start.
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  3. #3
    Site Founder MathGuru's Avatar
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    Graphing

    I would also suggest graphing this and getting an idea of how the curve can cross the x axis exactly three times. I'll try to attach a graph if I can.
    Attached Thumbnails Attached Thumbnails Real Roots-msp.gif  
    Last edited by MathGuru; April 15th 2005 at 02:01 PM.
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  4. #4
    Junior Member theprof's Avatar
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    0 < p < 32

    bye
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