[JEE Advanced 2016] let pi 6 theta pi 12 if alpha 1 beta 1 are the roots
Let $-\frac\pi6<\theta<-\frac\pi{12}$. If $\alpha_1>\beta_1$ are the roots of $x^2-2x\sec\theta+1=0$ and $\alpha_2>\beta_2$ are the roots of $x^2+2x\tan\theta-1=0$, then $\alpha_1+\beta_2$ equals
(a) $2(\sec\theta-\tan\theta)$
(b) $2\sec\theta$
(c) $-2\tan\theta$
(d) $0$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 4d ago
▲ 0
Correct answer: (c) $-2\tan\theta$
$\alpha_1=\sec\theta-\tan\theta$ (since $\tan\theta<0$) and $\beta_2=-\tan\theta-\sec\theta$, so $\alpha_1+\beta_2=-2\tan\theta$.
JEE Advanced 2016 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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