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If the equations $x^{2} + m x + 1 = 0$ and $(b - c) x^{2} + (c - a) x + (a - b) = 0$ have a common root, then

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$m = - 2$

$m = 0$

$m = 1$

$m = - 1$

answer is A.

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Detailed Solution

As $x = 1$ satisfies
$(b - c) x^{2} + (c - a) x + (a - b) = 0$
$x = 1$ must satisfy $x^{2} + m x + 1 = 0$
$\Rightarrow 1 + m + 1 = 0 \Rightarrow m = - 2$

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