alpha,beta are roots of the equation ax^2+bx+c=0,(a is not equal to zero) if a,b,c are real numbers and det=0
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Answer:
orrect option is
A
p
2
a
2
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
Step-by-step explanation:
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