Math, asked by sarthak153, 3 months ago

alpha and beta be the roots of equation ax2 + 2bx + c=0 and alpha plus omega and beta plus omega be those px2 + qx + r = 0​

Answers

Answered by Abhijeetroy
1

Step-by-step explanation:

α,β are roots of ax

2

+bx+c=0

∴α+β=

a

−b

,αβ=

a

c

D

1

=b

2

−4ac=a

2

(

a

2

b

2

a

4c

)

=a

2

((α+β)

2

−4αβ)

=a

2

(α−β)

2

γ,δ are roots of px

2

+qx+r=0

γ+δ=

p

−q

,γδ=

p

r

D

2

=q

2

−4pr=p

2

(

p

2

q

2

p

4r

)=p

2

((γ+δ)

2

−4γδ)

=p

2

((γ−δ)

2

)

α,β,γ,δ are in A.P.

∴α−β=γ−δ

∴D

1

:D

2

=a

2

:p

2

D

2

D

1

=

p

2

a

2

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