Given equation x sup2 lambda 2x 8 15 0 has both roots positive then calculate the value of...........

Quantitative Aptitude (CDS) Quadratic Equations

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Given equation x²-λ( 2x- 8)- 15=0 has both roots positive then calculate the value of λ.

λ∈ (15/8 ,3] ∪[ 5,∞)

λ∈ ( -∞ ,-3)

λ∈ [ 3 , 5 ]

λ∈ ( 3 , 5 )

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Explanation:

D ≥0 and ( α+β )>0 and (αβ)>0
This is the condition of both roots are positive.
So, D = b²-4ac ≥0 put values and we get λ∈ (-∞ ,3] ∪[ 5,∞).
and from ( α+β )>0 we get. λ∈ ( 0 , ∞ )
and from (αβ)>0 we get λ∈ [15/8,∞).
Combined these three we get λ∈ (15/8 ,3] ∪[ 5,∞)