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

Arithmetic Progression

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Geometric Progression

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Harmonic Progression

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Arithmetic - Geometric Progression

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Solution

The correct option is A Arithmetic Progression
Clearly X=1 is a solution
$∴$ Product of the roots $= \frac{a - b}{b - c}$
$∴ (1) (1) = \frac{a - b}{b - c}$
$\Rightarrow b - c = a - b$
$\Rightarrow 2 b = a + c \Rightarrow a, b, c a r e i n A . P$

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