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Byju's Answer
Standard XII
Mathematics
Graph of Quadratic Expression
If α and ...
Question
If
α
and
β
are the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
and
3
b
2
=
16
a
c
, then
A
α
=
4
β
or
β
=
4
α
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B
α
=
−
4
β
or
β
=
−
4
α
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C
α
=
3
β
or
β
=
3
α
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D
α
=
−
3
β
or
β
=
−
3
α
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Solution
The correct option is
D
α
=
3
β
or
β
=
3
α
Given that
(
α
,
β
)
are roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
and
3
b
2
=
16
a
c
.
.
.
.
.
(
i
)
∴
α
+
β
=
−
b
a
and
α
β
=
c
a
.
.
.
.
.
(
i
i
)
From eq
(
i
)
we get
2
b
.
b
=
16
a
.
c
⇒
⇒
3
(
b
a
)
2
=
16
(
c
a
)
(divide by
a
2
)
⇒
3
(
α
+
β
)
2
=
16
α
β
⇒
3
α
2
+
3
β
2
+
6
α
β
=
16
α
β
⇒
3
α
2
+
3
β
2
=
10
α
β
⇒
3
(
α
β
)
+
3
(
β
α
)
=
10
Let
α
β
=
x
Then,
3
x
+
3
x
=
10
⇒
3
x
2
−
10
x
+
3
=
0
⇒
3
x
2
−
9
x
−
x
+
3
=
0
⇒
3
x
(
x
−
3
)
−
1
(
x
−
3
)
=
0
⇒
(
x
−
3
)
(
3
x
−
1
)
=
0
⇒
x
=
1
3
,
3
⇒
α
β
=
1
3
,
3
∴
β
=
3
α
or
α
=
3
β
Suggest Corrections
0
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