Let the two roots be $\alpha _{1}$ and $\alpha _{2}$
For a quadratic equation $ax^2 +bx +c = 0$, sum of the roots $= -\frac{b}{a}$ and product of the roots $=\frac{c}{a}.$So,
$\alpha _{1}$ + $\alpha _{2}$ = (A - 3)
$\alpha _{1}$.$\alpha _{2}$ = -(A - 2)
We want $\alpha _{1}^{2}$ + $\alpha _{2}^{2}$ = 0
$\Rightarrow$ $\left ( \alpha _{1} + \alpha _{2} \right )^{2}$ - 2$\alpha _{1}$.$\alpha _{2}$ = 0
$\Rightarrow$ (A - 3)2 - 2(-(A - 2)) = 0
$\Rightarrow$ A2 - 4A + 5 = 0
$\Rightarrow$ A = 2 $\pm$ i
D is the answer