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. There are real roots only when $p^{2}-4 q \geqslant 0$
D. When $p>0$, there are three real roots
Let $f(x)=x|x|+p x+q=\left\{\begin{array}{l}x^{2}+p x+q, x \geqslant 0, \\ -x^{2}+p x+q, x<0 .\end{array}\right.$
Then $A, B$ are correct, $C$ is incorrect. For option $D$, take $p=-1, q=1$, we can see that $f(x)=0$ has only one real root. Therefore, the correct answers are $C, D$.