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Consider a region \( \mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^{2}: \mathrm{x}^{2} \leq \mathrm{y} \leq 2 \mathrm{x}\right\} \). if a line \( y=\alpha \) divides the area of region \( R \) into two equal parts,
\( \mathrm{P} \) then which of the following is true?

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(a) \( 3 \alpha^{2}-8 \alpha+8=0 \)
[JEE Main-2020 (September)]
(c) \( 3 \alpha^{2}-8 \alpha^{3 / 2}+8=0 \)
(b) \( \alpha^{3}-6 \alpha^{3 / 2}-16=0 \)
(d) \( \alpha^{3}-6 \alpha^{2}+16=0 \)
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