Consider \( a x^{4}+(7 a-2 b) x^{3}+(12 a-14 b-c) x^{2}-(24 b+7 c) x+1-12 c=0 \), has no real ro...

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Consider \( a x^{4}+(7 a-2 b) x^{3}+(12 a-14 b-c) x^{2}-(24 b+7 c) x+1-12 c=0 \), has no real roots and
\[
\begin{array}{c}
f_{1}(x)=\frac{\sqrt{\log _{(\pi+e)}\left(a x^{4}+(7 a-2 b) x^{3}+(12 a-14 b-c) x^{2}-(24 b+7 c) x+1-12 c\right)}}{\sqrt{a} \sqrt{-\operatorname{sgn}\left(1+a c+b^{2}\right)}} \\
f_{2}(x)=2 \log _{\sqrt{2}} \cos \left(\tan ^{-1}\left(\sin \left(\pi\left(\cos \left(\pi\left(x+\frac{7}{2}\right)\right)\right)\right)\right)\right) .
\end{array}
\]
Number of integers in range of \( f_{2}(x) \) is
(a) 0
(b) 1
(c) 2
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