I guess this requires a bit of additional knowledge about polynomial equations with real coefficients and complex roots.
A polynomial that has both z1 and z2 as its roots, must be of the form:
(z-z1)(z-z2)(...) = 0
If such an equation has only real coefficients, that implies that not only z1 must be a root, but also its conjugate z1*.
(I suspect that is somewhere in your notes.)
In other words, your equation must be of the form:
If you expand this, which coefficients do you get?