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Math Help - Solve all values for x

  1. #1
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    Solve all values for x

    Solve all possible values of x

    x^3-3x^2+4x-12=0

    Could someone do this question for me please, really urgent.
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  2. #2
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    Quote Originally Posted by Dean View Post
    Solve all possibl;e values of x

    [tex]x^3-3x^2+4x-12=0[tex]

    Could someone do this question for me please, really urgent.
    Hello,

    use factorization:

    x^3-3x^2+4x-12=0~\Longrightarrow~x^2(x-3) + 4(x-3) = 0~\Longrightarrow~(x-3)(x^2+4)=0

    Since x^2+4 > 0 there is only one real value for x: \boxed{x = 3}
    = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

    EDIT: You asked for all possible solutions. You didn't mention a domain so maybe imaginary solutions are possible for you too:

    (x-3)(x^2+4)=0 . A product of 2 factors is zero if one factor is zero:

    (x-3) = 0~\vee~(x^2+4)=0

    x = 3~\vee~x^2= -4

    x = 3~\vee~x= 2i~\vee~x = -2i
    Last edited by earboth; August 21st 2007 at 06:18 AM.
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