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Byju's Answer
Standard XII
Mathematics
Definition of Functions
If α, β, γ ...
Question
If
α
,
β
,
γ
are the roots of the equation
x
3
−
3
x
+
11
=
0
, what is the equation whose roots are
(
α
+
β
)
,
(
β
+
γ
)
and
(
γ
+
α
)
?
Open in App
Solution
given equation
x
3
−
3
x
+
11
=
0
α
+
β
+
γ
=
0
α
,
β
,
γ
are roots
α
β
+
β
γ
+
γ
α
=
−
3
of the equation
α
β
γ
=
−
11
if
α
+
β
,
β
+
γ
,
γ
+
α
are roots then
Equation say
a
x
3
+
b
x
2
+
c
x
+
d
=
0
(
α
+
β
)
+
(
β
+
γ
)
+
(
γ
+
α
)
=
−
b
/
a
.
2
(
α
+
β
+
γ
)
=
−
b
/
a
⇒
b
/
a
=
0
(
α
+
β
)
(
β
+
γ
)
+
(
β
+
γ
)
(
γ
+
α
)
+
(
γ
+
α
)
(
α
+
β
)
=
c
/
a
We know that
α
+
β
+
γ
=
0
∴
α
+
β
=
−
γ
β
+
γ
=
−
α
γ
+
α
=
−
β
(
−
γ
×
−
α
)
+
(
−
β
×
−
α
)
+
(
−
β
×
−
γ
)
=
c
/
a
α
β
+
β
γ
+
γ
α
=
c
/
a
⇒
c
/
a
=
−
3
(
α
+
β
)
(
β
+
γ
)
(
γ
+
α
)
=
−
d
/
a
−
α
β
γ
=
−
d
/
a
⇒
d
/
a
=
−
11
a
x
3
+
b
x
2
+
c
x
+
d
=
0
⇒
x
3
+
b
a
x
2
+
c
a
x
2
+
c
a
x
+
d
a
=
0
Req. Equation is
x
3
−
3
x
−
11
=
0
Suggest Corrections
3
Similar questions
Q.
If
α
,
β
,
γ
are the roots of the cubic
x
3
−
p
x
2
+
q
x
−
r
=
0
, find the equations whose roots are
(
β
+
γ
−
α
)
,
(
γ
+
α
−
β
)
,
(
α
+
β
−
γ
)
Q.
If
α
,
β
,
γ
are the roots of
a
x
3
+
b
x
2
+
c
x
+
d
=
0
and
∣
∣ ∣ ∣
∣
α
β
γ
β
γ
α
γ
α
β
∣
∣ ∣ ∣
∣
=
0
,
α
≠
β
≠
γ
, then find the equation whose roots are
α
+
β
−
γ
,
γ
+
α
−
β
,
β
+
γ
−
α
Q.
If
α
,
β
,
γ
are the roots of the equation
x
3
−
3
x
+
11
=
0
, then the equation whose roots are
(
α
+
β
)
,
(
β
+
γ
)
and
(
γ
+
α
)
is :
Q.
lf
α
,
β
,
γ
are the roots of
x
3
+
2
x
−
3
=
0
, then the transformed equation having the roots
α
β
+
β
α
,
β
γ
+
γ
β
,
γ
α
+
α
γ
is obtained by taking
x
=
Q.
Suppose
α
,
β
,
γ
are roots of
x
3
+
x
2
+
2
x
+
3
=
0
. If
f
(
x
)
=
0
is a cubic polynomial equation whose roots are
α
+
β
,
β
+
γ
,
γ
+
α
then
f
(
x
)
=
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