Let c be a real number, and let z_{1} and z_{2} be the two complex numbers satisfying the equation z^{2}-c z+10=0. Points z_{1}, z_{2}, \dfrac{1}{z_{1}}, and \dfrac{1}{z_{2}} are the vertices of (convex) quadrilateral \mathcal{Q} in the complex plane. When the area of \mathcal{Q} obtains its maximum possible value, c is closest to which of the following?
Answer Choices
A. 4.5
B. 5
C. 5.5
D. 6
E. 6.5