1.
Let pp and qq be real numbers such that p0p \neq 0, p3qp^3 \neq q and p3qp^3 \neq -q. If α\alpha and β\beta are non-zero complex numbers satisfying α+β=p\alpha+\beta=-p and α3+β3=q\alpha^3+\beta^3=q, then a quadratic equation having α/β\alpha/\beta and β/α\beta/\alpha as its roots is