If ' \( \alpha \) ' is a complex constant such that \( \alpha z^{2}+z+\bar{\alpha}=0 \) has a re....

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If ' \( \alpha \) ' is a complex constant such that \( \alpha z^{2}+z+\bar{\alpha}=0 \)
\( \mathrm{P} \)
has a real root, then
(1) \( \alpha+\bar{\alpha}=1 \)
(2) \( \alpha+\bar{\alpha}=0 \)
(3) \( \alpha+\bar{\alpha}=-1 \)
(4) The absolute value of the real root is ' 1 '.


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