Hi,
Can anyone please guide me how to solve this problem:
If α, b, g are the roots of the equation
3x^3─5x^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
After you have solved the original equation for the roots $\displaystyle \alpha \, \beta \, \gamma \;$ 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:
$\displaystyle \mbox{Let} P(z) \, \mbox{be a polynomial with the desired roots, then}\;$ $\displaystyle P(z) = (z-(r_{1}))(z-(r_{2}))(z-(r_{3}))\,$ $\displaystyle \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!