Question

Roots of the equation x² + ax + b = 0 are in the ratio 1:2 then​

Answer 1

Answer:

Let α,β be the roots of equation x2+px+q=0 and let γ,δ be the roots of equation x2+bx+c=0

Then, α+β=−p,αβ=q 

and γ+δ=−b,γδ=c 

Given, βα=δγ

Applying componendo-dividendo 

α−βα+β=γ−δγ+δ

⇒(α−β)2(α+β)2=(γ−δ)2(γ+δ)2

⇒α2+β2−2αβp2=γ2+δ2−2γδb2

⇒(α+β)2−4αβp2=