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Math Help - Advanced application to a cubic equation

  1. #1
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    Advanced application to a cubic equation

    Hi Everyone,
    This is a math problem I received during a math team meet as practice. I spent an hour on it with no luck. Does anyone have any ideas?

    The polynomial function f(x) = x^3 + ax^2 + bx + c has the following properties:
    1. At least two of its zeros are distinctive
    2. The sum of its zeros is twice the product of its zeros
    3. The sum of the squares of the zeros is three times the product of its zeros
    4. f(1) = 1
    Find the numerical value of c

    Any solutions?
    -ShadowKnight8702
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  2. #2
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Advanced application to a cubic equation

    Hint:

    Check this out:

    x^3-2.0329*10^-20 x^2-1.5695*10^-9 x+3.4235*10^-15

    or:

    f(x)=(-0.000038478 + x) (-2.1879*10^-6 + x) (0.000040666 + x)
    Last edited by MaxJasper; September 30th 2012 at 02:29 PM.
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  3. #3
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    Re: Advanced application to a cubic equation

    Quote Originally Posted by MaxJasper View Post
    Hint:

    Check this out:

    x^3-2.0329*10^-20 x^2-1.5695*10^-9 x+3.4235*10^-15



    or:

    f(x)=(-0.000038478 + x) (-2.1879*10^-6 + x) (0.000040666 + x)
    Is that really a hint? I think that makes it more confusing.
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