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If (1 + k) \tan ^2 x - 4 \tan x - 1 - k = 0 has real roots \tan x_1 and \tan x_2 , where \tan x_ 1 \neq \tan x_2  then

Option: 1

k^2 < 5 , k \neq -1


Option: 2

k^2 < 5


Option: 3

k^2 \leq 5 , k \neq -1


Option: 4

none of these 


Answers (1)

best_answer

As we have learnt in

 

Condition for Real and distinct roots of Quadratic Equation -

D= b^{2}-4ac> 0

- wherein

ax^{2}+bx+c= 0

is the quadratic equation

 

  

Since the given equation has distinct roots

    D > 0                             

Þ  16+4(1-k^2)>0\\\\ k^2 <5 \\\\                       

                alsok \neq -1

          If  k = –1        we will get only one solution, but we want two solutions

\    k^2 <5 , k \neq -1

Posted by

Deependra Verma

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