$f(x)= x^4 + ax^3+bx^2+cx+d$ is a polynomial with real coefficients and $f(2i)= f(2+i)=0$, what is the value of $a+b+c+d $?
This was a question I saw on internet but I don't want its solution, I just want to ask something about it. $2i$ and $2+i$ would be roots of $f(x)$ but the one who solved it also said that $-2i$ and $2-i$ were roots of it and I couldn't understand why, could you explain me please?
If $f$ is a polynomial with real coefficients and if $z \in \mathbb C$, then we have
$f( \overline{z})= \overline{f(z)}$.
Can you take it from here ?