Find the values of $K$, so that the quadratic equation ${ x }^{ 2 }+2\left( K-1 \right) x+K+5=0$ has atleast one positive root.

For a quadratic equation to have at least one positive root, either the product of roots is negative (c/a < 0) or the discriminant is non-negative and the sum of roots is positive. Here, c/a = K+5. If K+5 < 0, K < -5. Testing the vertex and boundary conditions for the quadratic, the range K <= -1 ensures the existence of a positive root.