Question

The ratio of roots of equation q2 + 5x+6=0 is 3: 4 then:​

Answer 1

Step-by-step explanation:

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=

Answer 2

Step-by-step explanation:

Let’s call the two roots p and q . Then:

2x2−5x+b=2(x−p)(x−q)=2x2−2(p+q)x+2pq

From the question, 2p=3q

Equating the coefficients:

−5=−2(p+q)→5=2p+2q=5q

2pq=b

From 1., q=1→p=1.5→pq=1.5

From 2., b=2pq=3

Answer: b=3