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Byju's Answer
Standard XII
Mathematics
Sign of Quadratic Expression
If 2x2 - 3x...
Question
If
(
2
x
2
−
3
x
+
1
)
(
2
x
2
+
5
x
+
1
)
=
9
x
2
, then equation has
A
four real roots
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B
two real and two imaginary roots
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C
four imaginary roots
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D
None of the above
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Solution
The correct option is
A
four real roots
(
2
x
2
−
3
x
+
1
)
(
2
x
2
+
5
x
+
1
)
=
9
x
2
(
2
x
2
−
3
x
+
1
)
(
2
x
2
+
5
x
+
1
)
x
2
=
9
(
2
x
2
−
3
x
+
1
)
x
(
2
x
2
+
5
x
+
1
)
x
=
9
(
2
x
−
3
+
1
x
)
(
2
x
+
5
+
1
x
)
=
9
(
2
x
+
1
x
−
3
)
(
2
x
+
1
x
+
5
)
=
9
Let
y
=
2
x
+
1
x
⇒
(
y
−
3
)
(
y
+
5
)
=
9
⇒
y
2
+
2
y
−
15
=
9
⇒
y
2
+
2
y
−
15
−
9
=
0
⇒
y
2
+
2
y
−
24
=
0
⇒
(
y
+
6
)
(
y
−
4
)
=
0
⇒
(
2
x
+
1
x
+
6
)
(
2
x
+
1
x
−
4
)
=
0
where
y
=
2
x
+
1
x
⇒
(
2
x
2
+
1
+
6
x
)
(
2
x
2
+
1
−
4
x
)
=
0
⇒
2
x
2
+
6
x
+
1
=
0
,
2
x
2
−
4
x
+
1
=
0
∴
x
=
−
6
±
√
36
−
4
×
2
×
1
2
×
2
,
x
=
4
±
√
16
−
4
×
2
×
1
2
×
2
∴
x
=
−
6
±
√
36
−
8
4
,
x
=
4
±
√
16
−
8
4
∴
x
=
−
6
±
√
28
4
,
x
=
4
±
√
8
4
∴
x
=
−
6
±
2
√
7
4
,
x
=
4
±
2
√
2
4
∴
x
=
−
3
±
√
7
2
,
x
=
2
±
√
2
2
∴
Roots are
{
−
3
+
√
7
2
,
−
3
−
√
7
2
,
2
+
√
2
2
,
2
−
√
2
2
}
Thus, there are four real roots.
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