If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation :

Question

$x^{2}+2 x-3=0$

$x^{2}+3 x-4=0$

$x^{2}+x-12=0$

$x^{2}+7 x+12=0$

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