Solve
Guides
Join / Login
Use app
Login
0
You visited us
0
times! Enjoying our articles?
Unlock Full Access!
Standard XIII
Mathematics
Question
If
α
,
β
∈
C
are the distinct roots, of the equation
x
2
−
x
+
1
=
0
, then
α
101
+
β
107
is equal to :
1
2
0
−
1
A
−
1
B
0
C
1
D
2
Open in App
Solution
Verified by Toppr
Given equation:
x
2
−
x
+
1
=
0
Solving it, we get
x
=
1
±
i
√
3
2
Or,
x
=
{
w
,
w
2
}
α
=
−
w
,
β
=
−
w
2
We know that,
w
3
=
1
, therefore
α
101
+
β
107
=
(
−
w
)
101
+
(
−
w
2
)
107
=
(
−
w
)
99
⋅
(
−
w
)
2
+
(
−
w
2
)
105
⋅
(
−
w
2
)
2
=
−
[
w
2
+
w
]
=
−
(
−
1
)
(sum of roots)
Hence,
α
101
+
β
107
=
1
Was this answer helpful?
42
Similar Questions
Q1
If
α
,
β
∈
C
are the distinct roots, of the equation
x
2
−
x
+
1
=
0
, then
α
101
+
β
107
is equal to :
View Solution
Q2
If
α
,
β
are roots of the quadratic equation
x
2
−
x
−
1
=
0
,
then the quadratic equation whose roots are
1
+
α
2
−
α
,
1
+
β
2
−
β
is
View Solution
Q3
If
α
and
β
are the roots of the equation
1
+
x
+
x
2
=
0
, then the matrix product
[
1
β
α
α
]
[
α
β
1
β
]
is equal to
View Solution
Q4
If
α
and
β
are the roots of the equation
x
2
+
p
x
+
2
=
0
and
1
α
and
1
β
are the roots of the equation
2
x
2
+
2
q
x
+
1
=
0
, then
(
α
−
1
α
)
(
β
−
1
β
)
(
α
+
1
β
)
(
β
+
1
α
)
is equal to
View Solution
Q5
If
α
,
β
are the roots of the equation
x
2
−
2
x
+
2
=
0
and if
c
o
t
θ
=
x
+
1
,
then
[
(
x
+
α
)
n
−
(
x
+
β
)
n
]
[
α
−
β
]
is equal to
View Solution