If α , β and γ are three consecutive terms of a non-constant G.P. Such that the equations…

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 αβ+γ is equal to:
  1. βγ
  2. αβ
  3. αγ
  4. 0

Solution

Given α, β,γ are in G.P.⇒β2=αγ
For the equation αx2+2βx+γ=0
D=4β2-4αγ=0
Hence roots of the equation are equal and equals to –βα=-γβ
Since given equation have common roots, hence -γβ must be a root of x2+x-1=0
⇒ γ2β2-γβ-1=0
⇒ γ2-γ β-β2=0
⇒ γ2=ββ+γ
⇒ γ.β2α=ββ+γ
⇒ αβ+γ=βγ

Asked in: JEE Main 2019 (12 Apr Shift 2)

Practice more Quadratic Equation questions on Aicharya