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Byju's Answer
Standard X
Mathematics
Solving Using Quadratic Formula When D>0
α, β are the ...
Question
α
,
β
are the solutions of
x
2
+
2
x
+
2
=
0
then
α
15
+
β
15
is
A
512
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B
256
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C
−
256
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D
−
512
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Solution
The correct option is
C
−
256
x
2
+
2
x
+
2
=
0
Here,
a
=
1
,
b
=
2
,
,
c
=
2
From quadratic formula,
x
=
−
2
±
√
2
2
−
4
×
2
×
1
2
×
1
⇒
x
=
−
2
±
2
i
2
=
−
1
±
i
Therefore,
α
=
−
1
+
i
⇒
α
2
=
(
−
1
+
i
)
2
=
−
2
i
β
=
−
1
−
i
⇒
β
2
=
(
−
1
−
i
)
2
=
2
i
Now,
α
15
+
β
15
=
(
α
2
)
7
⋅
α
+
(
β
2
)
7
⋅
β
=
(
−
2
i
)
7
(
−
1
+
i
)
+
(
2
i
)
7
(
−
1
−
i
)
=
(
−
2
)
7
(
−
i
)
(
−
1
+
i
)
+
2
7
(
−
i
)
(
−
1
−
i
)
=
2
7
i
(
−
1
+
i
)
+
2
7
i
(
1
+
i
)
=
2
7
i
(
−
1
+
i
+
1
+
i
)
=
2
7
i
⋅
2
i
=
2
8
⋅
(
−
1
)
=
−
256
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0
Similar questions
Q.
Let
α
and
β
be two roots of the equation
x
2
+
2
x
+
2
=
0
, then
α
15
+
β
15
is equal to :
Q.
Given equation
x
2
+
2
x
+
2
=
0
,
α
,
β
are the roots of the equation then
α
15
+
β
15
Q.
If
α
and
β
are roots of the quadratic equation
x
2
+
2
x
+
2
=
0.
Then
α
15
+
β
15
=
Q.
x
2
+
2
x
+
2
has
2
roots
(
α
,
β
)
then
α
15
+
β
15
=
?
Q.
x
2
+
2
x
+
2
=
0
has the roots as
α
and
β
then find
α
15
+
β
15
=
?
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