k=7
given a quadratic polynomial
ax^2+bx+c
the sum of the roots is given by -(b/a)
and the product of the roots as (c/a)
hence we get sum of roots as -(-(k+6)/1) and product of roots as (2(2k-1))/1
since the sum is equal to half the Product then we get
k+6=2k-1 and solving for k we get 7