If the roots of kx3−18x2−36x+8=0  are in H.P., then k =

The given equation is kx3−18x2−36x+8=0  given that roots are in A.P.now consider f(1x)=0 ⇒  k(1x)3−18(1x)2−36(1x)+8=0  ⇒8x3−36x2−18x+k=0  …. ( 1 )Now the roots are in A.P.i.e., a−d,a,a+d  ∴   sum of the roots : a−d+a+a+d=368 3a=368⇒a=32 ∴   a  is one root of the equation Eq. ( 1 )f(32)=0 ⇒8(32)3−36(32)2−18(32)+k=0  ⇒k=81