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Le α, β be the roots of x2 – x + p = 0 and γ, δ the roots of x2 – 4x + q = 0. If α, β, γ, δ are in G.P., then the integral values of p and q respectively, are
  • a)
    –2, –32
  • b)
    –2, 3
  • c)
    –6, 3
  • d)
    –6. – 32
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Le α, β be the roots of x2 – x + p = 0 and γ, &...
α, β, γ, δ in GP.
Let α = a, β = ar, γ = ar2, δ = ar3
a+ar = 1  &  ar2+ar= 4
a(1+r) = 1   ar2 (1 + 1) = 4
r2 = 4 = r = ±2 


satisfy given equations but p & q not integer for r = 2
⇒ r ≠ 2
∴ r = -2a = -1 ⇒ α = -1,β = 2,γ = -4,δ = 8
(-1)2-(-1)+P = 0 ⇒ p =-2
8,(-4)2-4(-4)+q = 0 ⇒ q = -32 
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Le α, β be the roots of x2 – x + p = 0 and γ, δ the roots of x2 – 4x + q = 0. If α, β, γ, δ are in G.P., then the integral values of p and q respectively, area)–2, –32b)–2, 3c)–6, 3d)–6. – 32Correct answer is option 'A'. Can you explain this answer?
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