Question

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

• A. AP
• B. GP
• C. HP
• D. None of these

Answer 1

Answer: (C)

Since, roots of the equation are equal.
$\therefore$ Discriminant $=0$
i.e., $b^2(c-a{)}^2-4ac(b-c)(a-b)=0$
$\Rightarrow b^2(c+a{)}^2-4abc(a+c)+4a^2{c}^2=0$
$\Rightarrow (b(a+c)-2ac{)}^2=0$
$\Rightarrow b=\frac{2ac}{a+c}$
$\Rightarrow a,b,c$ are in $HP$.