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HCF of $x^{2} + 1 & x^{4} + x^{2} + q$ is same then the value of $q$ is

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$- i$

$i$

answer is C.

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Detailed Solution

$f (x) = x^{2} + 1$

$g (x) = x^{4} + x^{2} + q$

The factors of $x^{2} + 1 is (x + i) (x - i)$

$g (i) = f (i) o r g (- i) = f (- i)$

$i^{4} + i^{2} + q = i^{2} + 1$

$1 - 1 + q = 0$

$q = 0$

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