Question

If the roots of the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ be equal, then $a,b,c$ are in

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

Answer 1

The correct option is C $A.P.$

The roots of the equation $(b-c)x^2+(c-a)x+(a-b)=0$ are equal.

Sum off the coefficients $(b-c)+(c-a)+(a-b)=0$

$\Rightarrow 1$ is the root of the equation.

i.e other root is also $1$.

$\therefore$ Product of roots $\frac{a-b}{b-c}=1$

$\Rightarrow 2b=a+c$

$\therefore a,b,c$ are in AP.

Hence, option C.