Find the set of values of k such that the expression 4x(x + k) − k(3k − 4) is positive for all x.

pramodpandey | Student

We have given





Now if

`(2x+k)^2-4k(k-1)>0 `


`i.e (2x+k)^2 >0`  always true.

We need only second term to be positive ie. `-4k(k-1)>=0`

either   `k>=0 and k-1<=0` 

ie. `0<=k<=1`          (i)

or   `k<0 and k-1>0`

`k<0 and k>1` 

This case is not possible.

Thus only solution is



In above answer ,let  x=1 ,k=-2

`(x+k/2)^2+k-k^2=(1-1)^2-2-4=-6 <0`

Thus above answer is not correct.

answer does not consider k=0,1

even it can verify that  k=0,1 satisfy the condition.