The integral value of k  for which the equation (k−2)x2+8x+k+4=0  has both the roots real, distinct and negative is

Given equation is  (k−2)x2+8x+k+4=0    …( 1 ) Given that roots are real and distinct, therefore, 82−4  (k−2)(k+4)>0    (∵b2−4ac>0) ⇒    16−  {k2+2k−8}>0 ⇒  k2+2k−24<0   ⇒  (k+6)(k−4)<0 ⇒    −60    (∵ S =sum of the roots, P = product of the roots )From ( 1 ): S=−8k−2 , P=k+4k−2 ⇒    −8k−2<0     and k+4k−2>0 ⇒    1k−2>0     and  k+4k−2>0 ⇒    k−2>0     and k+4k−2>0 ⇒    k−2>0    and k+4>0 ⇒    k>2  and k>−4    …. ( 3 )From  ( 2 ) and ( 3 ) :2