7. For the equation $x|x|+p x+q=0$, which of the following conclusions is incorrect?
(A) There are at most three real roots;
(B) There is at least one real root;
(C) Real roots exist only when $p^{2}-4 q \geqslant 0$;
(D) When $p>0$, there are three real roots.
7. $(C),(D)$.
(1) The equation $x|x|+p x+q=0$.
When $x \geqslant 0$, * becomes $x^{2}+p x+q=0$.
When $x<0$, * becomes $-x^{2}+p x+q=0$.
If $q>0$, (1) and (2) have at most one real root. If $q=0$, (1) and (2) have at most two real roots. If $q<0$, (1) has two real roots, one positive and one negative. (2) has two real roots, both positive. Since $q<0$, the negative root is an extraneous root of (1), so (1) and (2) have at most three real roots. If $q=0$, (1) and (2) have exactly three real roots $x_{1}=0, x_{2}=p, x_{3}=-p$. Therefore, * has at most three real roots, so (A) is correct.
(2) From (1) and (2) for $q>0, q<0$, we examine the equation
$$
x|x|-x+1=0,
$$

When $x>0$, $x^{2}-x+1=0$ has no real roots.
When $x<0$, $x^{2}-x-1=0$ has two real roots.
Therefore, the conclusion that $x|x|-x+1=0$ has three real roots is incorrect. (D) is also incorrect.
Therefore, (C) and (D) are both incorrect, choose (C), (D).