## Quadratic equation question

Please help me in solving the following question â€˜pâ€™ and â€˜qâ€™ are two distinct roots of the equation x^2 â€“ 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 ax_{2} + bx + c= 0
then

For the given equation xsum of the two roots = p + q = -b/a and product of the two roots = p .q = c/a

^{2}- 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 â€“ 2p =>q = 3p Putting in eq(1) we get 4p = 3pfor 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 p^{2}=>p = 0 or 4/3

^{2}+ q

^{2}= 160/9