4. Given the quadratic equation $x^{2}+p x+q=0$ with roots $x_{1} 、 x_{2}$. The conditions are:
(1) $p 、 q 、 x_{1} 、 x_{2}$ are all integers that leave a remainder of 1 when divided by 3;
(2) $p 、 q 、 x_{1} 、 x_{2}$ are all integers that leave a remainder of 2 when divided by 3;
(3) $p 、 q$ are integers that leave a remainder of 1 when divided by 3, and $x_{1} 、 x_{2}$ are integers that leave a remainder of 2 when divided by 3;
(4) $p 、 q$ are integers that leave a remainder of 2 when divided by 3, and $x_{1} 、 x_{2}$ are integers that leave a remainder of 1 when divided by 3.
The equation can only satisfy ( ).
(A)(1)
(B)(2)
(C) (3)
(D) (4)
4. A.

From $p+x_{1}+x_{2}=0$ we know that the equation does not satisfy conditions (3) and (4). From $q=x_{1} x_{2}$ we know that the equation does not satisfy condition (2).