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Byju's Answer
Standard IX
Mathematics
Factor Theorem
For polynomia...
Question
For polynomial
p
(
x
)
=
x
2
−
4
x
+
3
,
α
+
β
=
.................( where
α
a
n
d
β
are roots of polynomial.)
A
Positive fraction
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B
Negative integer
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C
Positive integer
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D
Zero
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Solution
The correct option is
C
Positive integer
Given polynomial:
p
(
x
)
=
x
2
−
4
x
+
3
Comparing above equation with standard quadratic polynomial
a
x
2
+
b
x
+
c
=
0
we get
a
=
1
,
b
=
−
4
Let
α
,
β
be roots of
p
(
x
)
∴
α
+
β
=
−
b
a
=
−
(
−
4
)
1
=
4
, which is a positive integer.
Hence, option C is correct.
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