KEAM 2013 Math Paper

Given, (α,β) are the roots of the equation
px2+qx+r=0
∴‌‌α+β=−‌

q

p

.....(i)
and ‌‌αβ=‌

r

p

....(ii)
Also given, α+β=4.....(iii)
From Eqs. (i) and (iii), we get
−‌

q

p

=4⇒q=−4p.....(iv)
Also, p,q and r are in AP.
∴‌‌p+r=2q
⇒‌‌p+r=−8p  [from Eq. (iv)]
⇒‌‌9p+r=0
⇒‌‌‌

r

p

=−9 ....(v)
From Eqs. (ii) and (v).
αβ=−9