The equation whose roots are $\sqrt{2}, - \sqrt{2}, 3 i, - 3 i$ is

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$x^{4} - 7 x^{2} + 18 = 0$

$x^{4} - 7 x^{2} - 18 = 0$

$x^{4} + 7 x^{2} + 18 = 0$

$x^{4} + 7 x^{2} - 18 = 0$

answer is A.

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Detailed Solution

$\begin{array}{l} x = \pm \sqrt{2} \Rightarrow x^{2} - 2; \Rightarrow x = \pm 3 i \\ \Rightarrow x^{2} + 9 are factors \\ ∴ (x^{2} - 2) (x^{2} + 9) = 0 \Rightarrow x^{4} + 7 x^{2} - 18 = 0 \end{array}$

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