If \( \operatorname{cosec}^{2} \alpha x^{2}+x+\left(\beta^{2}-\beta...

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If \( \operatorname{cosec}^{2} \alpha x^{2}+x+\left(\beta^{2}-\beta+\frac{1}{2}\right)=0 \) has real roots, then \( \sin ^{2} \alpha+\left(\cos \left(\sin ^{-1} \beta\right)\right)^{2} \) equals
(a) \( 3 / 4 \)
(b) \( 7 / 4 \)
(c) \( 11 / 4 \)
(d) \( 15 / 4 \)
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