4. If the equation with respect to $x$
$$
x^{2}+2 a x+7 a-10=0
$$

has no real roots, then the equation that must have real roots is ( ).
(A) $x^{2}+2 a x+3 a-2=0$
(B) $x^{2}+2 a x+5 a-6=0$
(C) $x^{2}+2 a x+10 a-21=0$
(D) $x^{2}+2 a x+2 a+3=0$
4. A.

From the equation $x^{2}+2 a x+7 a-10=0$ having no real roots, we get its discriminant $\Delta<0$, but this does not guarantee that $\Delta_{B} 、 \Delta_{C} 、 \Delta_{D}$ are non-negative.

Therefore, option $(A)$ must have real roots, while the other equations may not necessarily have real roots.