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CAT 2022 Slot 3 Paper
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© examsnet.com
Question : 50
Total: 66
If
(
3
+
2
√
2
)
is a root of the equation
a
x
2
+
b
x
+
c
=
0
and
(
4
+
2
√
3
)
is a root of the equation
a
y
2
+
m
y
+
n
=
0
where
a
,
b
,
c
,
m
and
n
are integers, then the value of
(
b
m
+
c
−
2
b
n
)
is
0
1
3
4
Validate
Solution:
a
,
b
,
c
,
m
and
n
are integers so if one root is
3
+
2
√
2
then the other root is
3
−
2
√
2
Sum of roots
=
6
=
−
b
a
or
b
=
−
6
a
Product of roots
=
1
=
c
a
or
c
=
a
a
,
b
,
c
,
m
and
n
are integers so if one root is
4
+
2
√
3
then the other root is
4
−
2
√
3
Sum of roots
=
8
=
−
m
∕
a
or
m
=
−
8
a
product of roots
=
4
=
n
∕
a
or
n
=
4
a
(
b
m
+
c
−
2
b
n
)
=
6
a
8
a
+
(
a
+
12
a
)
4
a
=
3
4
+
13
4
=
16
4
=
4
© examsnet.com
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