Equal roots..

D=0:....... so, b^2(b square) - 4ac=0...... b=k+1; a=k+4; c=1;......... on getting the answer from this equation factorise which gives the values for k= 5, -3.

$Clearly,\quad since\quad the\quad equation\quad has\quad equal\quad roots,\quad D(Discriminant)=0$

$So,\quad { (k+1) }^{ 2 }-4(k+4)(1)=0$

$\Longrightarrow { \quad }{ k }^{ 2 }+1+2k-4k-16=0$

$\Longrightarrow \quad { k }^{ 2 }-2k-15=0$

$\Longrightarrow \quad (k+3)(k-5)=0$

$which\quad gives\quad us\quad k=5\quad or\quad k=-3$