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Math Help - Factors

  1. #1
    Junior Member Fnus's Avatar
    Joined
    Nov 2006
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    48

    Factors

    Some help would be greatly appreciated, I'm at such a loss
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  2. #2
    Super Member malaygoel's Avatar
    Joined
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    A cubic equation has three linear factors.
    in this case,two are same
    hence
    x^3 + 3x^2 - 9x + c= (x-p)(x-p)(x-q)
    x^3 + 3x^2 - 9x + c= x^3-(2p+q)x^2+(2pq+p^2)x-p^2q
    comparing the coefficients,
    2p+q=-3...[1]
    2pq+p^2=-9...[2]
    p^2q=-c...[3]
    we solve first two equations for p and q
    from 1st equation q=-3-2p
    substituting in second 2p(-3-2p)=-9
    hence,after rearraging and simplifying p^2+2p-3=0
    which gives p=-3,1
    hence from first equation, p=-3,q=3 or p=1,q=-5
    if we substitute in third equation,we get c=-27,5

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    Malay
    Last edited by malaygoel; December 4th 2007 at 04:49 AM.
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