$T h e s e t o f p o s i t i v e v a l u e s o f λ f o r w h i c h x^{2} - (λ^{2} - 5 λ + 5) x + (2 λ^{2} - 3 λ - 4) = 0 h a s r o o t s w h o s e s u m a n d p r o d u c t a r e b o t h l e s s t h a n 1 i s$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$(- 1, \frac{5}{2})$

$(1, 4)$

$[1, \frac{5}{2}]$

$(1, \frac{5}{2})$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} L e t α, β a r e r o o t s o f \\ x^{2} - (λ^{2} - 5 λ + 5) x + (2 λ^{2} - 3 λ - 4) = 0 \\ ∴ α + β = λ^{2} - 5 λ + 5, α β = 2 λ^{2} - 3 λ - 4 \\ G i v e n α + β < 1 \\ \Rightarrow λ^{2} - 5 λ + 5 < 1 \\ \Rightarrow λ^{2} - 5 λ + 4 < 0 \\ \Rightarrow (λ - 4) (λ - 1) < 0 \Rightarrow λ \in (1, 4) - - (1) \\ a n d α β < 1 \\ \Rightarrow 2 λ^{2} - 3 λ - 5 < 0 \\ \Rightarrow (λ + 1) (2 λ - 5) < 0 \\ \Rightarrow λ \in (- 1, \frac{5}{2}) - - (2) \\ f r o m (1) & (2) \\ λ \in (1, \frac{5}{2}) \end{array}$