Question 4
We consider the polynomials $P(x)=x^{3}+A x^{2}+B x+C$, $Q(x)=3 x^{2}+2 A x+B$ ($x$ is the variable $A$, $B$, $C$ are parameters). Suppose that, yes $a, b, c$ They are the three roots of $P$, those of $Q$ They are $\frac{a+b}{2}$, $\frac{b+c}{2}$. Determine all possible polynomials $P, Q$.