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Byju's Answer
Standard X
Mathematics
Relationship between Zeroes and Coefficients of a Polynomial
If α and β ar...
Question
If
α
a
n
d
β
are the zeroes of the quadratic polynomial
2
x
2
−
8
x
+
4
, then the value of
α
β
+
β
α
+
2
(
1
α
+
1
β
)
+
3
α
β
is ___.
16
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Solution
The correct option is
A
16
Given,
f
(
x
)
=
2
x
2
−
8
x
+
4
.
Let
α
a
n
d
β
be its zeroes.
∴
α
+
β
=
8
2
=
4
a
n
d
α
β
=
4
2
=
2
Now,
α
β
+
β
α
+
2
(
1
α
+
1
β
)
+
3
α
β
=
α
2
+
β
2
α
β
+
2
(
α
+
β
α
β
)
+
3
α
β
=
(
α
+
β
)
2
−
2
α
β
α
β
+
2
(
α
+
β
α
β
)
+
3
α
β
[
(
α
+
β
)
2
=
α
2
+
β
2
+
2
α
β
]
=
(
4
)
2
−
2
×
2
2
+
2
(
4
2
)
+
3
×
2
= 6 + 4 + 6 = 16
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3
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