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Byju's Answer
Standard XII
Mathematics
Geometric Progression
In the quadra...
Question
In the quadratic equation
a
x
2
+
b
x
+
c
=
0
, if
Δ
=
b
2
−
4
a
c
, then
α
+
β
,
α
2
+
β
2
,
α
3
+
β
3
are?
Open in App
Solution
α
+
β
=
−
b
a
......(1)
α
2
+
β
2
=
(
α
+
β
)
2
−
2
α
β
=
(
−
b
a
)
2
−
2
c
a
α
2
+
β
2
=
b
2
−
2
a
c
a
2
.......(2)
α
3
+
β
3
=
(
α
+
β
)
(
α
2
−
α
β
+
β
2
)
=
(
−
b
a
)
(
b
2
−
2
a
c
a
2
−
c
a
)
α
3
+
β
3
=
−
b
3
−
3
a
b
c
a
3
........(3)
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Similar questions
Q.
In the quadratic equation
a
x
2
+
bx
+
c
=
0
, if
Δ
=
b
2
−
4
a
c
and
α
+
β
,
α
2
+
β
2
,
α
3
+
β
3
are in G.P. where
α
,
β
are the roots of
a
x
2
+
bx
+
c
=
0
, then
Q.
In the quadratic equation
a
x
2
+
b
x
+
c
=
0
,
Δ
=
b
2
−
4
a
c
a
n
d
α
+
β
,
α
2
+
β
2
,
α
3
+
β
3
,
are in G.P. where
α
,
β
are the root of
a
x
2
+
b
x
+
c
=
0
,
then
Q.
Let
α
,
β
be roots of the equation
a
x
2
+
b
x
+
c
=
0
and
Δ
=
b
2
−
4
a
c
. If
α
+
β
,
α
2
+
β
2
,
α
3
+
β
3
are in
G
P
, then
Q.
Let
α
and
β
be the zeros of
f
(
x
)
=
a
x
2
+
b
x
+
c
,
a
≠
0
and
Δ
=
b
2
−
4
a
c
. If
α
+
β
,
α
2
+
β
2
and
α
3
+
β
3
are in G.P., then :
Q.
If
α
,
β
are the roots of
a
x
2
+
b
x
+
c
=
0
and
α
+
β
,
α
2
+
β
2
,
α
3
+
β
3
are in G.P., where
△
=
b
2
−
4
a
c
, then
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