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:

Step-by-step solution

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