If one root of the equation (a−b)x2+ax+1=0 be double the other and if a∈R, then the greatest value of 8b, is

Let the roots be α and 2 α.. Then,α+2α=−aa−b and 2α2=1a−b⇒α=−a3(a−b) and α2=12(a−b)⇒a29(a−b)2=12(a−b)⇒2a2=9a−9b⇒2a2−9a+9b=0⇒ 81−72b>0                            [∵a∈R]⇒ b≤9/8Hence, the greatest value of 8b is 9 .