If a, b, c are in H.P., then the roots of the equationab−cx2+bc−ax+ca−b=0 are

We know that ab−c+bc−a+ca−b=0So x=1is a root of the given equation Let α be the other root.Then α×1=ca−bab−c⇒α=ca−bab−c=1b−1a1c−1b⇒α=1 ∵a,b,c    are in H.P ∴1a,1b,1care in A.P]   Thus, the given equation has equal roots.