If you solve the quadratic equation, roots will be $5+i, 5-i$, but those are in base $10$
We know sum of roots of quadratic equation = $\frac{-b}{a} = 10$
$\therefore$ $(4)_{b} +(7)_{b} = (10)_{b}$, since $4$ and $7$ are the roots of the equation
$4*b^0+7*b^0=1*b^1+0*b^0$
$b=11$
Option D) is correct