If α , β are the roots of x 2 − 3 x + λ = 0 ( λ ∈ R ) and α < 1 < β , then the true set of values of λ equals

Let f ( x ) = x 2 − 3 x + λ \ Clearly f ( 1 ) < 0 ⇒ 1 − 3 + λ < 0 ⇒ λ < 2 ⇒ λ ∈ ( − ∞ , 2 )

Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationLocation of rootsMedium2 min

MathematicsMediumsingle choice

If $α, β$ are the roots of $x^{2} - 3 x + λ = 0 (λ \in R)$ and $α < 1 < β$ , then the true set of values of $λ$ equals

Answer:

Solution:

Let $f (x) = x^{2} - 3 x + λ$ \ Clearly $f (1) < 0$

$\Rightarrow 1 - 3 + λ < 0 \Rightarrow λ < 2 \Rightarrow λ \in (- \infty, 2)$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Location of roots

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