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Byju's Answer
Standard XII
Mathematics
Range
If α, β, ...
Question
If
α
,
β
,
γ
are the roots of
x
3
−
x
2
+
8
x
+
6
=
0
the
(
1
+
α
)
(
1
+
β
)
(
1
+
γ
)
=
A
4
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B
12
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C
14
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D
24
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Solution
The correct option is
A
4
x
3
−
x
2
+
8
x
+
6
=
0
Roots are
α
,
β
,
γ
α
+
β
+
γ
=
1
α
β
+
β
γ
+
γ
α
=
8
α
β
γ
=
−
6
(
1
+
α
)
(
1
+
β
)
(
1
+
γ
)
=
(
1
+
α
+
β
+
α
β
)
(
1
+
γ
)
=
1
+
α
+
β
+
γ
+
α
β
+
β
γ
+
γ
α
+
α
β
γ
=
1
+
1
+
8
−
6
=
4
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0
Similar questions
Q.
If
α
,
β
,
γ
are the roots of
x
3
+
p
x
2
+
q
=
0
where
q
≠
0
then
Δ
=
∣
∣ ∣ ∣
∣
1
/
α
1
/
β
1
/
γ
1
/
β
1
/
γ
1
/
α
1
/
γ
1
/
α
1
/
β
∣
∣ ∣ ∣
∣
equals
Q.
If
α
,
β
,
γ
are the roots of the equation
x
3
−
3
x
2
+
2
x
−
1
=
0
, then the value of
(
1
−
α
)
(
1
−
β
)
(
1
−
γ
)
is:
Q.
If
α
,
β
,
γ
are the roots of
x
3
+
a
x
2
+
b
=
0
,
b
≠
0
then the determinant
Δ
, where
Δ
=
∣
∣ ∣ ∣ ∣
∣
1
α
1
β
1
γ
1
β
1
γ
1
α
1
γ
1
α
1
β
∣
∣ ∣ ∣ ∣
∣
equals
Q.
If
α
,
β
,
γ
are roots of
x
3
+
x
2
−
5
x
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then
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α
]
+
[
β
]
+
[
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]
Q.
If
α
,
β
,
γ
are roots of
x
3
−
x
2
−
1
=
0
the value of
1
+
α
1
−
α
+
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+
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1
−
β
+
1
+
γ
1
−
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=
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