AMC 10B 2006 Problem 14

Let a and b be the roots of the equation x^{2}-m x+2=0. Suppose that a+(1 / b) and b+(1 / a) are the roots of the equation x^{2}-p x+q=0. What is q ?

Answer Choices
A. \dfrac{5}{2}
B. \dfrac{7}{2}
C. 4
D. \dfrac{9}{2}
E. 8