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Byju's Answer
Standard XII
Mathematics
Range of Quadratic Expression
Let P x = ax ...
Question
Let
P
(
x
)
=
a
x
2
+
b
x
+
8
is a quadratic polynomial. If the minimum value of
P
(
x
)
is
6
at
x
=
2
,
then
A
a
=
1
2
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B
b
=
−
1
2
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C
a
=
2
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D
b
=
−
2
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Solution
The correct options are
A
a
=
1
2
D
b
=
−
2
−
b
2
a
=
2
4
a
=
−
b
…
(
1
)
P
(
2
)
=
4
a
+
2
b
+
8
=
6
4
a
+
2
b
=
−
2
…
(
2
)
Using
(
1
)
and
(
2
)
b
=
−
2
,
a
=
1
2
Suggest Corrections
11
Similar questions
Q.
Let
P
(
x
)
=
a
x
2
+
b
x
+
8
is a quadratic polynomial. If the minimum value of
P
(
x
)
is
6
at
x
=
2
,
then
Q.
Let
p
(
x
)
=
a
x
2
+
b
x
+
8
this quadratic polynomial if the min value of the p(x) i.e
6
when
x
=
2
and find the values of
a
and
b
Q.
If 2 is a zero of the polynomial
p
(
x
)
=
x
3
−
a
x
2
+
b
x
+
c
,
then which of the following equations is true?
Q.
Let
p
(
x
)
=
a
x
2
+
b
x
+
c
be a quadratic polynomial. It can have at most
Q.
For a quadratic polynomial
p
(
x
)
=
a
x
2
+
b
x
+
c
,
α
+
β
=
2
and
α
β
=
−
8
where
α
,
β
are zeroes of
p
(
x
)
.
∴
The value of
a
,
b
and
c
is ________ respectively.
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