Question

If the two roots of the equation x² - px +q = 0 be a and b then p²ab=q(a+b)² . True or false

Answer 1

Answer:

0

Step-by-step explanation:

Correct option is

A

0

Let α,β be the roots of equation x

2

+px+q=0 and let γ,δ be the roots of equation x

2

+bx+c=0

Then, α+β=−p,αβ=q

and γ+δ=−b,γδ=c

Given,

β

α

=

δ

γ

Applying componendo-dividendo

α−β

α+β

=

γ−δ

γ+δ

⇒

(α−β)

2

(α+β)

2

=

(γ−δ)

2

(γ+δ)

2

⇒

α

2

+β

2

−2αβ

p

2

=

γ

2

+δ

2

−2γδ

b

2

⇒

(α+β)

2

−4αβ

p

2

=

(γ+δ)

2

−4γδ

b

2

⇒

p

2

−4q

p

2

=

b

2

−4c

b

2

⇒p

2

c−b

2

q=0`