let $\displaystyle \alpha , \beta, \gamma, \delta $ be the roots of the polynomial equation.

$\displaystyle x^{4}+5x^{3}+3x^{2}-x+2=0 $

calculate $\displaystyle \alpha^{2} +\beta^{2} +\gamma^{2} + \delta^{2} $

..my thoughts... polynomial can be written as $\displaystyle (x-\alpha)(x-\beta)(x-\gamma)(x-\delta) $ expand this and equate? but will this be general for every polynomial irrespective of the signs of the coefficients? thanks appreciate its alot of latex!