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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

`tan alpha + tan beta =(2lambda)/3 , tan alpha tan beta = 1/3`
`therefore cot (alpha+beta)=1/2 rArr (tan alpha + tan beta)/(1-tan alpha tan beta)=2`
`rArr ((2lambda)/3)/(1-1/3)=2 rArr lambda=2`
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