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# The quadratic equation whose roots are $\pm\;i\sqrt{7}$is

$\begin{array}{1 1}(1)x^{2}+7=0&(2)x^{2}-7=0\\(3)x^{2}+x+7=0&(4)x^{2}-x-7=0\end{array}$

$\alpha= i \sqrt 7$
$\eta= -i \sqrt 7$
Sum $\alpha +\beta=i \sqrt 7 - i \sqrt 7=0$
Product $\alpha \beta = i \sqrt 7 \times i \sqrt 7=0$
$\qquad= -i^2 7 =7$
The quadratic equation whose roots are $\alpha , \beta$ is
$x^2$-(sum of the roots)x+product of the roots=0x^2-(\alpha+\beta)x +\alpha \beta=0x^2-ox+7=0x^2+7=0\$