Question

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

• A. Arithmetic progression
• B. Geometric progression
• C. Harmonic progression
• D. Arithmetico-Geometric progression

Answer 1

The correct option is A Arithmetic progression

$\therefore$ Product of the roots =$\frac{a-b}{b-c}$
$\therefore$ (1) (1) =$\frac{a-b}{b-c}$
$\Rightarrow$ b-c= a-b
$\Rightarrow$ 2 b =a+b $\Rightarrow$ a,b,c are in A.P