Solution
= Solution
For any smooth projective curve of <genus> $g$, a <canonical divisor> has degree $2g-2$. If this plane curve had genus two, part (ii) would imply
$$
d(d-3)=2,
$$
so $d^2-3d-2=0$. The <quadratic discriminant> is $17$, which is not a <perfect square>, so the equation has no integral solution. Thus \b[a smooth projective plane curve cannot have genus two], as recorded by <no smooth plane curve has genus two>.