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Quadratic Equation and Inequalities question

2016 · Shift 1 · Q31

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JEE Advanced
Mathematics
Quadratic Equation and Inequalities
2016 · Shift 1 · Q31

Quadratic Equation and Inequalities question

2016 · Shift 1 · Q31

JEE AdvancedMathematicsQuadratic Equation and InequalitiesMCQ+3 / −1

Let

- {\pi \over 6} \lt \theta \lt - {\pi \over {12}}.

Suppose

{\alpha _1}

and

{\beta_1}

are the roots of the equation

{x^2} - 2x\sec \theta + 1 = 0

and

{\alpha _2}

and

{\beta _2}

are the roots of the equation

{x^2} + 2x\,\tan \theta - 1 = 0.If\,{\alpha _1} \gt {\beta _1}

and

{\alpha _2} \gt {\beta _2},

then

{\alpha _1} + {\beta _2}

equals

A
$2\left( {\sec \theta - \tan \theta } \right)$
B
$2\,\sec \,\theta$
C
$- 2\tan \theta$
D
$0$

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