UPSEE Solved Model Paper 4

The given equations are
2x2 + (λ − 1) x + 8 = 0 ... (1)
and x2 − 8x + λ + 4 = 0 ... (2)
These equations have real roots if
(λ−1)2 − 4 ⋅2 ⋅ 8 ≥ 0
and (−8)2 − 4 (λ + 4) ≥ 0
i.e., if λ2 − 2λ − 63 ≥ 0 and − 4 λ ≥ − 48
i.e., if (λ − 9) (λ + 7) ≥ 0 and λ ≤ 12
i.e. if λ ≤ − 7 or λ ≥ 9 and λ ≤ 12
⇒ λ ∊ (- ∞ , - 7] ∪ [9 , 12]
but in question it as given that λ ≥ 0
so λ ∊ [9 , 12]
so greatest value of λ is 12