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The value of a for which the equations $x^{3} + a x + 1 = 0$ , $x^{4} + a x^{2} + 1 = 0$ have a common root is

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-2

answer is B.

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Detailed Solution

$x^{4} + a x^{2} + 1 = 0 \to (1)$

$x^{3} + a x + 1 = 0 \to (2)$

$(1) - (2) \Rightarrow x^{4} - x^{3} + a x^{2} - a x = 0$

$\Rightarrow x^{3} (x - 1) + a (x^{2} - x) = 0$

$\Rightarrow (x - 1) x [x^{2} + a] = 0$

$\Rightarrow x = 0, 1$

$x = 1 \Rightarrow a = - 2$

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