Let \( p \) and \( q \) be real numbers such that \( p=0, p^{3}=q \) and \( p^{3} \) \( =-q \). ...
Let \( p \) and \( q \) be real numbers such that \( p=0, p^{3}=q \) and \( p^{3} \) \( =-q \). If \( \alpha \) and \( \beta \) are nonzero complex numbers satisfying \( \alpha \) \( +\beta=-p \) and \( \alpha^{3}+\beta^{3}=q \), then a quadratic equation having \( \frac{\alpha}{\beta} \) and \( \frac{\beta}{\alpha} \) as its roots is
(a) \( \left(p^{3}+q\right) x^{2}-\left(p^{3}+2 q\right) x+\left(p^{3}+q\right)=0 \)
(b) \( \left(p^{3}+q\right) x^{2}-\left(p^{3}-2 q\right) x+\left(p^{3}+q\right)=0 \)
(c) \( \left(p^{3}-q\right) x^{2}-\left(5 p^{3}-2 q\right) x+\left(p^{3}-q\right)=0 \)
(d) \( \left(p^{3}-q\right) x^{2}-\left(5 p^{3}+2 q\right) x+\left(p^{3}-q\right)=0 \)
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