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CGP EDU Academic Team
Published on: August 14, 2026
α, β be the root of x 2 –3x + a = 0 and γ, δ are the root of x 2 –12x + b = 0 and numbers α, β, γ, δ (in order) form an increasing G.P., then
Text Solution
Verified by ExpertsThe correct answer is:
C
x 2 –3x + a = 0 α, β
x 2 –12x + b = 0 γ, δ
α, β, γ, δ are in G.P. so a, ar, ar 2 , ar 3 α + β = 3 = a + ar … (1)
γ + δ = 12 = ar
2 + ar 3 …. (2)
γ 2 (a + ar) = 12
γ 2 = 4 ⇒ γ = ± 2
Increasing G.P. so r = 2
a + 2a = 3 from (1)
a = 1
α = 1, β = 2
γ = 4, δ = 8
a = αβ , b = γδ
α = 2, b = 32
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