Question

If the quadratic equation $a(b-c) x^2+$ $b(c-a) x+c(a-b)=0$, where $a, b, c$ are distinct real numbers and $a b c \neq 0$, has equal roots, then $a, b, c$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

Answer: (C)

As 1 is a root of the equation and equation has equal roots, the other root must be 1 . Thus we have
$1=\text { product of roots }=\frac{c(a-b)}{a(b-c)} $
$\Rightarrow a(b-c)=c(a-b) $
$\Rightarrow b=\frac{2 a c}{a+c} $
$\Rightarrow a, b, c \text { are in H.P. } $