Question

The set of possible values of λ for which

x² – (λ² – 5λ + 5) x + (2λ² – 3λ – 4) = 0 has roots, whose sum and product are both less than 1, is –

• A. $\left( –1,\frac{5}{2} \right)$
• B. (1, 4)
• C. $\left\lbrack 1,\frac{5}{2} \right\rbrack$
• D. $\left( 1,\frac{5}{2} \right)$

Answer 1

Answer: (D)

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

Answer 2

λ² – 5λ + 5 < 1 2λ² – 3λ – 4 < 1

λ² – 5λ + 4 < 0 λ² – 3λ – 5 < 0

(λ – 1) (λ – 4) < 0 (λ + 1) (2λ – 5) < 0

λ∈ (1, 4) λ ∈ (–1, 5/2)

common part λ ∈ (1, 5/2)