If α , β and γ are three consecutive terms of a non-constant G.P. Such that the equations α x 2 + 2 β x + γ = 0 and x 2 + x - 1 = 0 have a common root, then α β + γ is equal to:

Question

If α , β and γ are three consecutive terms of a non-constant G.P. Such that the equations α x 2 + 2 β x + γ = 0 and x 2 + x - 1 = 0 have a common root, then α β + γ is equal to:, β γ, α β, α γ, 0

MARKS App · Accepted Answer

Given α , β , γ are in G.P. ⇒ β 2 = α γ For the equation α x 2 + 2 β x + γ = 0 D = 4 β 2 - 4 α γ = 0 Hence roots of the equation are equal and equals to – β α = - γ β Since given equation have common roots, hence - γ β must be a root of x 2 + x - 1 = 0 ⇒ γ 2 β 2 - γ β - 1 = 0 ⇒ γ 2 - γ β - β 2 = 0 ⇒ γ 2 = β β + γ ⇒ γ . β 2 α = β β + γ ⇒ α β + γ = β γ

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