If  the roots of 24x3−26x2+9x−1=0  are in H.P.,  then the roots are

The given equation is f(x)=24x3−26x2+9x−1=0  Given roots  are in H.P Now consider,f(1x)=0 ⇒x3−9x2+26x−24=0 Now the roots  are in A.P.⇒  roots are (a−d),a,(a+d) ∴  sum of the roots : 3a=9 ⇒a=3 Product of the roots : a(a2−d2)=24 ⇒3(9−d2)=24          (∵  a=3)  ⇒d=1 ∴  (a−d)=2     a=3    (a+d)=4 ∴  The required roots are  1a−d,1a,1a+d= 12,13,14