MathematicsMedium210×since 2002Q3483Let \int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}. Then eα\mathrm{e}^\alphaeα and e−α\mathrm{e}^{-\alpha}e−α are the roots of the equation :A2x2−5x+2=02 x^2-5 x+2=02x2−5x+2=0Bx2−2x−8=0x^2-2 x-8=0x2−2x−8=0C2x2−5x−2=02 x^2-5 x-2=02x2−5x−2=0Dx2+2x−8=0x^2+2 x-8=0x2+2x−8=0Check answerSkip