Form equation with derived roots

If $\alpha$ and $\beta$ are the roots of $x^2+px+q=0$, form the equation whose roots are $(\alpha -\beta {)}^2$ and $(\alpha +\beta {)}^2$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. IX. The Theory of Quadratic Equations, Examples IX.a, No. 24