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Byju's Answer
Standard XIII
Mathematics
Cubic Polynomial
If one of the...
Question
If one of the roots of the quadratic equation
x
2
−
x
−
1
=
0
is
α
, then its other root is
A
α
3
−
3
α
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B
α
3
−
2
α
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C
α
2
−
2
α
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D
α
2
−
3
α
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Solution
The correct option is
A
α
3
−
3
α
Let
β
be other root of equation
x
2
−
x
−
1
=
0
∴
α
+
β
=
−
−
1
1
=
1
⇒
β
=
1
−
α
⋯
(
i
)
∵
α
is a root of,
x
2
−
x
−
1
=
0
∴
α
2
−
α
−
1
=
0
⇒
α
2
=
α
+
1
⋯
(
i
i
)
Now to find the correct expression, let's do hit and trial method.
α
2
−
3
α
=
α
+
1
−
3
α
=
1
−
2
α
=
β
−
α
≠
β
α
3
−
2
α
=
α
2
⋅
α
+
1
−
2
α
=
α
(
α
+
1
)
−
2
α
=
α
2
+
α
−
2
α
=
α
+
1
−
α
=
1
≠
β
α
2
−
2
α
=
α
+
1
−
2
α
=
1
−
α
=
−
β
≠
β
α
3
−
3
α
=
α
.
α
2
−
3
α
=
α
(
α
+
1
)
−
3
α
=
α
2
+
α
−
3
α
=
α
+
1
+
α
−
3
α
=
1
−
α
=
β
Hence other root
β
=
α
3
−
3
α
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0
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