Question bank/JEE Main/Mathematics
JEE MainMathematicsModerateQuadratic Equations
If λ is real and (λ^2 + λ - 2)x^2 + (λ +2) x < 1 for all real
x, then set of all values of λ is
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Suppose that (λ^2 + λ - 2)x^2 + (λ + 2) x - 1 < 0
For all real x,
λ^2 + λ - 2 < 0 and (λ + 2)^2 + 4(λ^2 + λ - 2) < 0
- 2 < λ < 1 and (λ+ 2) (5λ -2) < 0
- 2 < λ < 1 and -2 < λ < [IMAGE] These inequalities imply λ ∈ [-2, 2/5)
For all real x,
λ^2 + λ - 2 < 0 and (λ + 2)^2 + 4(λ^2 + λ - 2) < 0
- 2 < λ < 1 and (λ+ 2) (5λ -2) < 0
- 2 < λ < 1 and -2 < λ < [IMAGE] These inequalities imply λ ∈ [-2, 2/5)
Source: Grass-G / M-03 Paper 1 Mathematics 21-8-2020_Final.docx
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