If α, β and γ are three consecutive terms of a non-constant G.P. such that the equations αx² + 2βx + γ = 0 and x² + x - 1 = 0 have a common root, then α(β + γ) is equal to

Correct option is A. βγ
αx² + 2βx + γ = 0
Let β = αt, γ = αt²
∴ αx² + 2αtx + αt² = 0
⇒ x² + 2tx + t² = 0
⇒ (x + t)² = 0
⇒ x = -t
It must be root of equation x² + x - 1 = 0
∴ t² - t - 1 = 0 (1)
Now α(β + γ) = α(αt + αt²) = α²(t + t²)
Option 1 βγ = αt × αt² = α²t³ = α²(t² + t) (from equation 1).