4. Given equation A: $x^{2}+p_{1} x+q_{1}=0$, equation B: $x^{2}+p_{2} x+q_{2}=0$, where $p_{1} 、 p_{2} 、 q_{1} 、 q_{2}$ are all real numbers, and satisfy $p_{1} p_{2}=2\left(q_{1}+q_{2}\right)$. Then $(\quad)$.
(A) Both A and B must have real roots
(B) Neither A nor B has real roots
(C) At least one of A and B has real roots
(D) Whether A and B have real roots cannot be determined