Let $\alpha $ and $\beta $ be two real roots of the equation$(k + 1){\tan ^2}x - \sqrt 2 \cdot {\rm{ }}\lambda \tan x = (1 - k),$ where $k( \ne - 1)$ and ${\rm{ }}\lambda $ are real numbers. If ${\tan ^2}(\alpha {\rm{ }} + {\rm{ }}\beta ) = 50$ , then a value of $\lambda $ is

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

Let

\alpha

and

\beta

be two real roots of the equation

(k + 1){\tan ^2}x - \sqrt 2 \cdot \mathrm{ }\lambda \tan x = (1 - k),

where

k( \ne - 1)

and

\mathrm{ }\lambda

are real numbers. If

{\tan ^2}(\alpha \mathrm{ } + \mathrm{ }\beta ) = 50

, then a value of

\lambda

View answer and explanation

Correct option: B

Option B (10) is correct because it is one of the values of

\lambda

obtained by solving the trigonometric equation using the given condition

{\tan ^2}(\alpha + \mathrm{ }\beta ) = 50

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