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Let alpha, beta be two real roots...

Let ` alpha, beta ` be two real roots of the equation ` cot ^ 2 x - 2 lamda cot x + 3 = 0 , lamda in R ` . If ` cot ( alpha + beta ) = (1)/(2)` , then value of ` lamda ` is :

A

1

B

2

C

` ( 1 ) /(2) `

D

` (3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`cot^(2) x - 2 lamdba cot x + 3 = 0 : (##VMC_JEE_REV_TST_30_E03_010_S01.png" width="80%">
`rArr " " 3 tan^(2) x + 1 = 0 : (##VMC_JEE_REV_TST_30_E03_010_S02.png" width="80%">
`tan alpah + tan beta = ( 2lambda)/(3), " " tan alpha tan beta = (1)/(3)`
`therefore " " cot (alpha + beta) = (1)/(2) " "rArr " " (tan alpha + tan beta)/(1 - tan alpha beta ) = 2 `
`rArr ((2lambda)/(3))/(1- (1)/(3)) = 2 " "rArr lambda = 2`
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