For which polynomials $p(x)$ is $p(p(x))+p(x)$=$x^4+3x^2+3$, for all $x \in \mathbb{R}$ For which polynomials $p(x)$ is $p(p(x))+p(x)$=$x^4+3x^2+3$, for all $x \in \mathbb{R}$
Since the power of the right hand side is 4, $p(x)$ has to be 2.
So I assumed a solution of: $p(x)=ax^2+bx+c$ and then i put it in $p(p(x))+p(x)$ and got:
$a(ax^2+bc+c)^2+b(ax^2+bx+c)+c+ax^2+bx+c=x^4+3x^2+3$
To find the coefficients I tried $x=0$ and got 
$ac^2+bc+2c=3$. But here I'm stuck, how do I go from here? 

The polynomials
$$Ax^5+Bx^4+Cx^3+Dx^2+Ex+F$$
and 
$$ax^5+bx^4+cx^3+dx^2+ex+f$$
are equal for all $x$ if and only if
$$A=a\\B=b\\C=c\\D=d\\E=e\\F=f$$
