Comprehension \( 2 a x^{3}+x^{2}+2 a x+1=0 \), where \( a \in R \). Also, range of \( f(x)=x+\fr...

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Comprehension
\( 2 a x^{3}+x^{2}+2 a x+1=0 \), where \( a \in R \). Also, range of \( f(x)=x+\frac{1}{x} \) is \( (-\infty,-2] \cup[2, \infty) \)

If equation has at least two distinct positive real roots, then all possible value of \( a \) are
(a) \( \left(-\infty,-\frac{1}{4}\right) \)
(b) \( \left(\frac{5}{4}, \infty\right) \)
(c) \( \left(-\infty,-\frac{3}{4}\right) \)
\( (d)\left(\frac{-5}{4}, \infty\right) \)
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