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Byju's Answer
Standard XII
Mathematics
Relation between Roots and Coefficients for Higher Order Equations
If α , β , γ ...
Question
If
α
,
β
,
γ
are the roots of
x
3
+
3
x
2
+
4
x
+
5
=
0
, then which of the following is/ are true.
A
∑
β
2
γ
2
=
−
14
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B
∑
1
α
=
−
4
5
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C
∑
α
2
=
1
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D
∑
α
=
3
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Solution
The correct option is
C
∑
α
2
=
1
α
+
β
+
γ
=
−
3
α
β
+
β
γ
+
γ
α
=
4
,
α
β
γ
=
−
5
∑
1
α
=
α
β
+
β
γ
+
γ
α
α
β
γ
=
−
4
5
∑
α
2
=
(
α
+
β
+
γ
)
2
−
2
(
α
β
+
β
γ
+
γ
α
)
=
9
−
8
=
1
∑
β
2
γ
2
=
(
α
β
+
β
γ
+
γ
α
)
2
−
2
α
β
γ
(
α
+
β
+
γ
)
=
16
−
2
(
−
5
)
(
−
3
)
=
−
14
Suggest Corrections
0
Similar questions
Q.
If
α
,
β
,
γ
are the roots of
x
3
+
3
x
2
+
4
x
+
5
=
0
, then which of the following is/ are true.
Q.
If
α
,
β
,
γ
are the roots of
x
3
+
3
x
2
−
4
x
+
2
=
0
then the equation whose roots are
1
α
β
,
1
β
γ
,
1
γ
α
Q.
If
α
,
β
,
γ
are the roots of
x
3
−
3
x
2
+
4
x
−
7
=
0
, then
(
α
+
2
)
(
β
+
2
)
(
γ
+
2
)
=
Q.
If
α
,
β
,
γ
are the roots of the equation
x
3
+
4
x
+
1
=
0
, then
(
α
+
β
)
−
1
+
(
β
+
γ
)
−
1
+
(
γ
+
α
)
−
1
=
Q.
If
α
,
β
and
γ
are roots of the cubic equation
x
3
+
3
x
2
+
3
x
+
2
=
0
, then the value of
(
α
+
β
+
γ
)
, is:
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Relation between Roots and Coefficients for Higher Order Equations
Standard XII Mathematics
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