I am having difficulty with a particular question, not sure how to approach it (well the chapter in the textbook is on the relation between the roots and coeeficients eg. sums products of roots) so it will use that approach i guess.

If $\displaystyle x^{4}+4x^{3}+mx^{2}+nx+9=(x^{2}+bx+c)^{2}$ for all values of $\displaystyle x$, find all possible vales of b and c and the corresponding vales of m and n

Thanks for your help