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Math Help - Forming Equations Using Roots

  1. #1
    Senior Member
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    Exclamation Forming Equations Using Roots

    Hi

    How do I do this question:

    The equation 3x^3 + 6x^2 - 4x + 7 = 0 has roots a,b,c. Fnd the equation with roots a + b, a + c, b+ c.

    I can do simple ones e.g. roots 1/a, 1/b, 1/c but I failed at this one
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  2. #2
    MHF Contributor red_dog's Avatar
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    Let x_1=a, \ x_2=b, \ x_3=c. Then x_1+x_2+x_3=-2

    y_1=x_2+x_3=-x_1-2

    y_2=x_1+x_3=-x_2-2

    y_3=x_1+x_2=-x_3-2

    Let y=-x-2\Rightarrow x=-y-2

    Replace x in the equation:

    3(-y-2)^3+6(-y-2)^2-4(-y-2)+7=0\Rightarrow -3y^3-12y^2-8y+15=0
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