The set of values of \( a \) for which \( x^{2}+a x+\tan ^{-1}\left(x^{2}-4 x+5\right) \) \( +...

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The set of values of \( a \) for which \( x^{2}+a x+\tan ^{-1}\left(x^{2}-4 x+5\right) \) \( +\cot ^{-1}\left(x^{2}-4 x+5\right)=0 \) has at least one solutions is
(a) \( (-\infty,-\sqrt{2 \pi}] \cup[\sqrt{2 \pi}, \infty) \)
(b) \( (-\infty, \sqrt{2 \pi}) \cup(\sqrt{2 \pi}, \infty) \)
(c) \( R \)
(d) None of these
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