11.2. Find all values of the parameter $a$ for which the equation $\sqrt{x^{2}-2 x-3}\left(x^{2}-3 a x+2 a^{2}\right)=0$ has exactly three roots.
Answer: $-1 \leq a<-\frac{1}{2}$ or $\frac{3}{2}<a \leq 3$. Solution. See problem 10.2.