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Math Help - Finding Equation

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    6

    Finding Equation

    Hi,

    Can anyone please guide me how to solve this problem:

    If α, b, g are the roots of the equation

    3x^35x^2 + 2x + 5 = 0


    Find the equation whose roots are


    α^2 + b^2 + bα , b^2 + g^2 + gb, g^2 + α^2 + gα
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  2. #2
    Senior Member Twig's Avatar
    Joined
    Mar 2008
    From
    Gothenburg
    Posts
    396

    Hi

    After you have solved the original equation for the roots  \alpha \, \beta  \, \gamma \; then you have the "formula" for generating new
    roots for another equation.
    You insert the these values in the formulas you gave, and you can now
    do the following:
     \mbox{Let} P(z) \, \mbox{be a polynomial with the desired roots, then}\; P(z) = (z-(r_{1}))(z-(r_{2}))(z-(r_{3}))\, \mbox{where the r:s, are the roots given by the formula you have.}
    I think this is they way to do it, but I am kinda in a hurry so if I am wrong, I apologize

    GL!
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