Here's one thought: if the coefficients of the polynomial are all real, then any complex roots come in complex-conjugate pairs. Hence, -4+2i is also a root of F, F', and F''. That means you technically have 7 equations and 7 unknowns (the unknowns being the coefficients). I would just start plugging in numbers into the functions you have, and start cranking away. It's a fair bit of algebra, looks like. What do you get?