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$ax^3 +bx^2 + cx + d= 0$

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?

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Use Vieta's formulas

and the following identity:

$$a^2b^2+b^2c^2+c^2a^2=(ab+bc+ca)^2-2abc(a+b+c)$$

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