F(z) = z^2-z-2F(z)=z2−z−2
F(z)F(z) is a quadratic function with real coefficients.
I'm not claiming that the following constitutes an "essay". Nor would I know how to write one on F(z)F(z). Also, I do not understand what is meant by, "Need to relate what?". Nevertheless, I will set out some of the attributes of F(z)F(z) below.
F(z)F(z) factorizes into (z-2)(z+1)(z−2)(z+1)
:. the zeros of F(z) are z=2 or -1
The graph of F(z) will be a parabola with axis of symmetry z=1/2
Since the coefficient of z^2 is >0 -> F(z) will have a minimum values on its axis of symmetry.
Therefore, the minimum value of F(z) is F(1/2)
Thus, F_min = F(1/2) = 1/4-1/2-2 = -9/4
The graph of F(z) is shown below - where z is the horizontal axis.
graph{x^2-x-2 [-3.798, 4.97, -2.53, 1.855]}
As an aside, using the nomenclature F(z) usually indicates that z is a complex variable. In this case, however, {F(z),z} in RR
