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Byju's Answer
Standard XIII
Mathematics
Sign of Quadratic Expression
The range of ...
Question
The range of
a
for which
x
2
−
a
x
+
1
−
2
a
2
is always positive for all real values of
x
, is
A
(
−
2
3
,
2
3
)
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B
[
−
2
3
,
2
3
]
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C
(
−
∞
,
1
)
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D
(
−
2
3
,
2
3
]
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Solution
The correct option is
A
(
−
2
3
,
2
3
)
x
2
−
a
x
+
1
−
2
a
2
>
0
,
∀
x
∈
R
So,
D
<
0
⇒
(
−
a
)
2
−
4
(
1
−
2
a
2
)
<
0
⇒
9
a
2
−
4
<
0
⇒
a
2
<
4
9
∴
a
∈
(
−
2
3
,
2
3
)
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1
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