UPSEE Solved Model Paper 5

Since, (λ2+λ−2)x2 + (λ + 2) x - 1 < 0
Fro all x ∊ R then D < 0 and a < 0
∴ (λ+2)2+4(λ2+λ−2) < 0 and λ2+λ−2 < 0
⇒ 5λ2+8λ−4 < 0 and λ2+λ−2 < 0
⇒ (5λ - 2) (λ + 2) 0 and (λ + 2) (λ - 1) < 0
⇒ - 2 < λ <

2

5

and - 2 < λ < 1
⇒ - 2 < λ <

2

5

⇒ λ∊ (−2,

2

5

)