Question

If α, β and γ are three consecutive terms of a non-constant G.P. such that the equations αx³ + 2βx + γ = 0 and x² + x – 1 = 0 have a common root, then α(β + γ) is equal to :
(A) αγ (B) 0
(C) αβ (D) βγ

Answer 1

Answer:

sorry I dunno.............

Answer 2

Answer:

ANSWER

αx^2+2βx+γ=0

Let β=αt,γ=αt ^2

∴αx^2+2αtx+αt^2=0

⇒x^2+2tx+t^2 =0

⇒(x+t)^2=0

⇒x=−t

It must be root of equation x

2

+x−1=0

∴t

2

−t−1=0....(1)

Now

α(β+γ)=α^2(t+t^2 )

Option 1 βγ=αt⋅αt^2 =α