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Byju's Answer
Standard X
Mathematics
Discriminant
If both roots...
Question
If both roots of quadratic equation
(
α
+
1
)
x
2
−
2
(
1
+
3
α
)
x
+
1
+
8
α
=
0
are real and distinict, the
α
be-
A
-2
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B
1
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C
2
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D
3
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Solution
The correct option is
A
-2
(
α
+
1
)
x
2
−
2
(
1
+
3
α
)
x
+
1
+
8
α
=
0
Here,
a
=
α
+
1
b
=
−
2
(
1
+
3
α
)
c
=
1
+
8
α
If both roots are real and distinct,
D
>
0
⇒
b
2
−
4
a
c
>
0
⇒
(
−
2
(
1
+
3
α
)
)
2
−
4
(
1
+
α
)
(
1
+
8
α
)
>
0
⇒
4
(
1
+
9
α
2
+
6
α
)
−
4
(
1
+
9
α
+
8
α
2
)
>
0
⇒
4
(
1
+
9
α
2
+
6
α
−
1
−
9
α
−
8
α
2
)
>
0
⇒
α
2
−
3
α
>
0
⇒
α
(
α
−
3
)
>
0
⇒
α
∈
(
−
∞
,
0
)
∪
(
3
,
∞
)
Hence among the given values,
α
will be
−
2
.
Hence the correct answer is
(
A
)
−
2
.
Suggest Corrections
0
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