Let $pandq$ be real numbers such that $p\ne 0,p^3\ne q,and{p}^3\ne -q\dot{}$ If $\alpha and\beta$ are nonzero complex numbers satisfying $\alpha +\beta =-pand{\alpha }^2+{\beta }^2=q$ , then a quadratic equation having $\alpha /\beta and\beta /\alpha$ as its roots is $\left(p^3+q\right)x^2-\left(p^3+2q\right)x+\left(p^3+q\right)=0$$\left(p^3+q\right)x^2-\left(p^3-2q\right)x+\left(p^3+q\right)=0$$\left(p^3+q\right)x^2-\left(5p^3-2q\right)x+\left(p^3-q\right)=0$$\left(p^3+q\right)x^2-\left(5p^3+2q\right)x+\left(p^3+q\right)=0$

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