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

True

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False

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Solution

The correct option is A True
$D = 0$
$(c - a)^{2} - 4 (b - c) (a - b) = 0$
$c^{2} + a^{2} + 4 b^{2} - 2 a c - 4 a b + 4 a c - 4 b c = 0$
$(c + a - 2 b)^{2} = 0$
$c + a - 2 b = 0$
$2 b = a + c$

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