$ax^3 +bx^2 + cx + d= 0$
If the roots are $\alpha$ $\beta$ and $\gamma$,
Is there any relationship between the sum of the squares of the roots and the coefficients of the quadratic equation..
In other words:
$\alpha^2$$\beta^2$+$\beta^2$$\gamma^2$+$\gamma^2$$\alpha^2$= something to do with the coefficients?
Best Answer
Use Vieta's formulas
and the following identity:
$$a^2b^2+b^2c^2+c^2a^2=(ab+bc+ca)^2-2abc(a+b+c)$$