If f (x) = ( - α) (x - β),
then f (λ) = (λ - α) (λ - β) = ive as the two factors are of opposite signs by given conditions.
Also roots must be real
∴Δ≥0⇒8(λ2+λ+12)
=8[(λ+12)2+14] is +ive, which is true.
Now f (λ) = -ive
⇒2λ2−2(2λ+1)λ+λ(λ+1)<0
or −λ2−λ<0orλ(λ+1)>0
or λ<−1orλ>0