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If roots of the equation (a - b)x² + (c - a)x+(b - c) = 0 are equal, then a, b and c are in

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detailed solution

Correct option is A

Since, roots of the equation
$(a - b) x^{2} + (c - a) x + (b - c) = 0$
$∴ Discriminant, B^{2} - 4 AC = 0$
$\begin{array}{lr} \Rightarrow (c - a)^{2} - 4 (a - b) (b - c) = 0 \\ \Rightarrow a^{2} + 4 b^{2} + c^{2} + 2 ac - 4 ab - 4 bc = 0 \\ \Rightarrow (a + c - 2 b)^{2} = 0 \Rightarrow a + c = 2 b \end{array}$
Hence ,a, b, c ate in AP

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