The quadratic equation \( z^{2}+\left(p+i p^{\prime}\right) z+q+i q...

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The quadratic equation \( z^{2}+\left(p+i p^{\prime}\right) z+q+i q^{\prime}=0 \); where \( p, p^{\prime}, q, q^{\prime} \) are all real.
(A) if the equation has one real root then \( q^{\prime 2}-p p^{\prime} q^{\prime}+q p^{\prime 2}=0 \).
\( \mathrm{P} \)
(B) if the equation has two equal roots then \( p p^{\prime}=2 q^{\prime} \).
W
(C) if the equation has two equal roots then \( p^{2}-p^{\prime 2}=4 q \)
(D) if the equation has one real root then \( p^{\prime 2}-p p^{\prime} q^{\prime}+q^{\prime 2}=0 \).
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