If \( \alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta} \) are zeros of \( f(x)=x^{2}-5 x-a \), whe...

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If \( \alpha+\frac{1}{\alpha}, \beta+\frac{1}{\beta} \) are zeros of \( f(x)=x^{2}-5 x-a \), where \( \alpha, \beta \in(0, \infty) \) for all \( x \in R \), then the complete set of values of \( a \) is
(A) \( \left[-6, \frac{25}{4}\right] \)
(B) \( \left[\frac{-25}{4}, 6\right] \)
(C) \( \left[\frac{-25}{4},-6\right] \)
(D) \( \left(\frac{-25}{4},-6\right) \)
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