For what value of k, $x^{2} + 2(k-1)x + k+5$ has at least one positive root?
Approach: Case I : Only $1$ positive root, this implies $0$ lies between the roots, so $$f(0)<0$$ and $$D > 0$$
Case II: Both roots positive. It implies $0$ lies behind both the roots. So, $$f(0)>0$$ $$D≥0$$ Also, abscissa of vertex $> 0 $
I did the calculation and found the intersection but its not correct. Please help. Thanks.