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Byju's Answer
Standard XII
Mathematics
Integration by Partial Fractions
If α-β=√b2-...
Question
If
(
α
−
β
)
=
√
b
2
−
4
a
c
a
and
α
β
=
c
a
then find
α
3
−
β
3
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Solution
α
3
−
β
3
=
(
α
−
β
)
(
α
2
+
α
β
+
β
2
)
=
(
α
−
β
)
(
α
2
+
β
2
+
α
β
)
We have
(
α
−
β
)
2
=
α
2
+
β
2
−
2
α
β
or
α
2
+
β
2
=
(
α
−
β
)
2
+
2
α
β
α
3
−
β
3
=
(
α
−
β
)
(
(
α
−
β
)
2
+
2
α
β
+
α
β
)
=
(
α
−
β
)
(
(
α
−
β
)
2
+
3
α
β
)
=
√
b
2
−
4
a
c
a
⎛
⎜
⎝
(
√
b
2
−
4
a
c
a
)
2
+
3
c
a
⎞
⎟
⎠
=
√
b
2
−
4
a
c
a
(
b
2
−
4
a
c
a
2
+
3
c
a
)
=
√
b
2
−
4
a
c
a
(
b
2
−
4
a
c
+
3
c
a
a
2
)
=
√
b
2
−
4
a
c
a
(
b
2
−
a
c
a
2
)
=
(
√
b
2
−
4
a
c
)
(
b
2
−
a
c
)
a
3
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0
Similar questions
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
Q.
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?
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.
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.
If
α
,
β
are the roots of
a
x
2
+
b
x
+
c
=
0
(
a
≠
0
)
and
α
+
β
,
α
2
+
β
2
,
α
3
+
β
3
are in
G
.
P
.
, then the value of
c
⋅
Δ
is
(where
Δ
=
b
2
−
4
a
c
)
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