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Math Help - Finding an Equation of a Polynomial

  1. #1
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    Finding an Equation of a Polynomial

    The roots of the equation 6x^3+17x^2-5x-6=0 is represented by a,b, and c (from least to greatest). Determine an equation whose roots are a+b, a/b, and ab.
    I got the roots of the first equation, which are x+3, 2x+1, and 3x-2, but I don't get how to do the second part. I think you list three cubic equations and solve for a,b, and c, but what do you do with d?

    Thanks!
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  2. #2
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    Re: Finding an Equation of a Polynomial

    Quote Originally Posted by Dragon08 View Post
    The roots of the equation 6x^3+17x^2-5x-6=0 is represented by a,b, and c (from least to greatest). Determine an equation whose roots are a+b, a/b, and ab.
    I got the roots of the first equation, which are x+3, 2x+1, and 3x-2, but I don't get how to do the second part. I think you list three cubic equations and solve for a,b, and c, but what do you do with d?

    Thanks!
    x+3, 2x+1, and 3x-2 are not the roots, they're factors of the polynomial. (x+3)(2x+1)(3x-2) = 6x^3+17x^2-5x-6

    Get the roots by setting each of these factors equal to zero: x+3=0, 2x+1=0, and 3x-2=0. Solve each for x.
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  3. #3
    Super Member TheChaz's Avatar
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    Re: Finding an Equation of a Polynomial

    (From my post at MMF)
    x + 3 is a FACTOR; the corresponding root is x = -3
    2x + 1 is a factor <=> x = -1/2 is a root
    3x - 2 is a factor <=> x = 2/3 is a root.

    And there we have them... a, b, and c.
    a + b = -3 + -1/2 = -7/2
    For this to be a root, (2x + 7) will be a factor.
    Then for a/b = 6 to be a root, (x - 6) will be a factor.
    Likewise for ab.

    Then multiply the factors together!

    http://www.mymathforum.com/viewtopic...t=24007#p95919
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