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Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If ( λ 2 + λ – 2) x 2 + ( λ + 2) x< 1 for all x ∈ R then λ belongs to the interval -

(–2, 1)

None of these

Text Solution

Verified by Experts

The correct answer is:

( λ 2 + λ – 2) x 2 + ( λ + 2) x – 1 < 0 for all x ∈ R if D < 0 and

a < 0, i.e., ( λ + 2) 2 + 4 ( λ 2 + λ – 2) < 0 and λ 2 + λ – 2 < 0.

5 λ 2 + 8 λ – 4 < 0 and λ 2 + λ – 2 < 0

⇒ (5 λ – 2) ( λ + 2) < 0 and ( λ + 2) ( λ – 1) < 0

–2 < λ < and –2 < λ < 1

i.e., –2 < λ < or λ ∈

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