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Quadratic equation question

Please help me in solving the following question ‘p’ and ‘q’ are two distinct roots of the equation x^2 – pqx + 2(q-p) = 0 What is the value of p^2 + q ^2 Given that x is not equal to 0. a. 160/9 b. 169/9 c. 144/9 d. 140/9

let p and q be the two roots

let p and q be the two roots of the equation ax2 + bx + c= 0 then

sum of the two roots = p + q = -b/a and product of the two roots = p .q = c/a
For the given equation x2 - pq x + 2(q-p) = 0 Sum of the two roots = p + q = -(-pq) = pq ------------(1) And product of the two roots = pq = 2(q-p) ------------(2) 
From eq(1) and eq(2) p + q = 2q – 2p 
                    =>q = 3p
Putting in eq(1)  we get
                     4p = 3p2
                   =>p = 0 or 4/3
for p =0, we get q =0 which contradicts the given condition that the two roots are distinct so p = 4/3 and q = 4 Thus p2 + q2 = 160/9