Finding Equation

mailquark · #1 $Old$ November 13th, 2008, 04:07 PM

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

Twig · #2 $Old$ November 15th, 2008, 02:20 AM

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!