λ2α , β are the roots of the equation x 2 – 3x + a = 0 and γ , δ are the roots of the equation x 2 – 12x + b = 0. If α , β , γ , δ form an increasing, GP, then (a, b) is equal to-
Text Solution
Verified by ExpertsC
Since α , β , γ , δ form an increasing GP.
So αδ = βγ where α < β < γ < δ …(i)
We have, x 2 – 3x + a = 0
⇒ x = 
(3 ± 
)
Also α < β
Hence, α = 
(3 – 
)
and β = 
(3 + 
)
Similarly, from x 2 – 12x + b = 0
⇒ x = 
Since, γ < δ
∴ γ = 
(12 – 
)
and δ = 
(12 + 
)
Substituting these values of α , β , γ , δ in Equation. (i)
(3 – 
) . 
(12 + 
)
= 
(3 + 
). 
(12 – 
).
Only the option (2, 32) satisfy the equation.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems