Let, the roots of the quadratic equation x2+px+q=0 is (α,β) Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e., Product of roots q=α.β=6×2=12 ...(i) and B starts with a wrong value of q and gets the roots as 2 and −9. But this time p is correct. i.e., Sum of roots p=α+β=−9+2=−7 ...(ii) (α−β)2=(α+β)2−4αβ =(−7)2−4.12=49−48=1 [From equations (i) and (ii)] ⇒ α−β=1 ....(iii) From equations (ii) and (iii), α=−3andβ=−4 which is correct roots.