If roots x₁ and x₂ of the equation x^2-4 a x+1=0 satisfy x₁ a and x₂ 0 , then a [ 1 k , x ), k must be

Step-by-step solution

D 0 a^2 1 4 a - 1 2 or a 1 2 Case -I: If a - 1 2 , then a is negative and x₁ a, x₂ 0 atleast one root must be positive either both roots are positive or exactly one root is positive. Now x ^2-4 ax +1=0 . can not have both roots positive. Since sum of the roots =4 a 0 Again exactly one root can not be positive since product 0 a - 1 2 is not possible Case-II: if a 1 2 , then x₁ - 1 2 , x₂ 0 x ₁+ x ₂ 0 ta 0 a 1 2 So a [ 1 2 , ) k =2