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

Arithmetic progression

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Geometric progression

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Harmonic progression

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Arithmetico-Geometric progression

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Solution

The correct option is A Arithmetic progression
$∴$ 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+b $\Rightarrow$ a,b,c are in A.P

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