CDS Model Paper 5 Mathematics

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.