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AP EAPCET 06-Jul-2022 Shift 2 Paper
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© examsnet.com
Question : 12
Total: 160
If
a
,
b
,
c
,
d
are real numbers such that
a
<
b
<
c
<
d
, then the roots of the equation
(
x
−
a
)
(
x
−
c
)
+
2
(
x
−
b
)
(
x
−
d
)
=
0
are
Real & need not be distinct
Real and distinct
Non-real and distinct
Non-real and need not be distinct
Validate
Solution:
👈: Video Solution
Here,
(
x
−
a
)
(
x
−
c
)
+
2
(
x
−
b
)
(
x
−
d
)
=
x
2
−
(
a
+
c
)
x
+
a
c
+
2
[
x
2
−
(
b
+
d
)
x
+
b
d
]
=
x
2
−
(
a
+
c
)
x
+
a
c
+
2
x
2
−
2
(
b
+
d
)
x
+
2
b
d
=
3
x
2
−
(
a
+
2
b
+
c
+
2
d
)
+
a
c
+
2
b
d
D
=
b
2
−
4
a
c
=
(
a
+
2
b
+
c
+
2
d
)
2
−
12
(
a
c
+
2
b
d
)
=
[
(
a
+
2
d
)
+
(
2
b
+
c
)
]
2
−
12
(
a
c
+
2
b
d
)
=
[
(
a
+
2
d
)
−
(
2
b
+
c
)
]
2
+
4
(
a
+
2
d
)
(
2
b
+
c
)
−
12
(
a
c
+
2
b
d
)
=
[
(
a
+
2
d
)
−
(
2
b
+
c
)
]
2
+
4
a
c
+
8
a
b
+
16
b
d
+
8
c
d
−
12
a
c
−
24
b
d
=
[
(
a
+
2
d
)
−
(
2
b
+
c
)
]
2
−
8
a
c
−
8
b
d
+
8
a
b
+
8
c
d
=
[
(
a
+
2
d
)
−
(
2
b
+
c
)
]
2
+
8
(
c
−
b
)
(
d
−
a
)
As,
a
<
b
<
c
<
d
,
(
c
−
b
)
(
d
−
a
)
>
0
∴
Roots are real and distinct.
© examsnet.com
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