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Thread: Factors

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

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

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