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Math Help - polynomial cubic roots

  1. #1
    Junior Member
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    polynomial cubic roots

    Solve the equation 4xcubed + 32xsquared + 79x + 60 = 0 given that one root is equal to the sum of the other two

    Here is my working out so far

    Let the roots be alpha, beta and gamma
    alpha + beta = gamma

    AND you know that

    alpha + beta + gamma = (-b/a) = (-8)
    alpha x beta x gamma = (-d/a) = (-15)
    alphabeta + alphagamma + betagamma = (79/4)

    i would realli like some help on how to proceed from here ?
    i just need to find wat alpha, beta and gamma are and am having alot of difficulty ><"" thankyouu for any help !! =D
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  2. #2
    MHF Contributor
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    West Malaysia
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    Quote Originally Posted by THSKluv View Post
    Solve the equation 4xcubed + 32xsquared + 79x + 60 = 0 given that one root is equal to the sum of the other two

    Here is my working out so far

    Let the roots be alpha, beta and gamma
    alpha + beta = gamma

    AND you know that

    alpha + beta + gamma = (-b/a) = (-8)
    alpha x beta x gamma = (-d/a) = (-15)
    alphabeta + alphagamma + betagamma = (79/4)

    i would realli like some help on how to proceed from here ?
    i just need to find wat alpha, beta and gamma are and am having alot of difficulty ><"" thankyouu for any help !! =D

    let a , b and y be 3 roots of this cubic equation .

    a+b+y=-8 ( the sum of roots ) --- 1

    aby=-15 ( the product of roots ) --- 2

    a=b+y ( one roots is the sum of the other 2 roots ) -- 3

    from 1 , b+y=-8-a

    substitute into 3 , a=-8-a , a=-4

    Then go back to 1 and 2 again .

    -4+b+y=-8

    b+y=-4 -- 4

    -4by==-15

    by=15/4 -- 5

    then u can solve the simultaneous equation (4 and 5) to get b and y .

    Note that both b and y can be -2.5 and -1.5 but not at the same time . Lets say if you put b=-2.5 , then y has to be -1.5 and vice versa .
    Last edited by mathaddict; June 26th 2009 at 08:53 PM. Reason: forgot about the other 2 roots .
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