If \( 2 x^{3}+a x^{2}+b x+4=0(a \) and \( b \) are positive real \(...

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If \( 2 x^{3}+a x^{2}+b x+4=0(a \) and \( b \) are positive real
\( \mathrm{P} \) numbers) has three real roots.

W
The minimum value of \( a^{3} \) is
(a) 108
(b) 216
(c) 432
(d) 864
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