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

Question

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

MARKS Content Team · Accepted Answer

Correct answer: (A) βγ. Given α, β,γ are in G.P.⇒β^2=αγ For the equation αx^2+2βx+γ=0 D=4β^2-4αγ=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=ββ+γ ⇒ γ.(β^2)/(α)=ββ+γ ⇒ αβ+γ=βγ

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:

Solution

Relevant Questions

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:

Solution

Relevant Questions

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: