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IIT JEE Advanced 2006 Paper 1
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© examsnet.com
Question : 115
Total: 120
If
x
2
–
10
a
x
–
11
b
=
0
have roots
c
and
d
and
x
2
–
10
c
x
–
11
d
=
0
have roots
a
and
b
. Find
a
+
b
+
c
+
d
.
Your Answer:
Validate
Solution:
c, d are roots of
x
2
−
10
a
x
−
11
b
=
0
∴
c
+
d
=
1
0
a
,
c
d
=
−
1
1
b
c
2
−
10
a
c
−
11
b
=
0
→
1
a
,
b
are roots of
x
2
−
10
c
x
−
11
d
=
0
a
+
b
=
1
0
c
,
a
b
=
−
1
1
d
a
2
−
1
0
a
c
−
1
1
d
=
0
→
2
a
+
b
+
c
+
d
=
1
0
(
a
+
c
)
⇒
b
+
d
=
9
(
a
+
c
)
abcd
=
121
bd
∴
a
c
=
121
1
−
2
⇒
(
c
2
−
a
2
)
−
11
(
b
−
d
)
=
0
c
2
−
a
2
=
1
1
(
b
−
d
)
1
+
2
⇒
a
2
+
c
2
−
2
0
a
c
−
1
1
(
b
+
d
)
=
0
(
a
+
c
)
2
−
22
a
c
−
99
(
a
+
c
)
=
0
(
a
+
c
)
2
−
99
(
a
+
c
)
−
2662
=
0
(
a
+
c
)
2
−
(
121
−
22
)
(
a
+
c
)
−
122
<
22
=
0
(
a
+
c
+
2
2
)
(
a
+
c
−
1
2
1
)
=
0
∴
a
+
c
=
121
a
+
b
+
c
+
d
=
1
0
(
a
+
c
)
∴
a
+
b
+
c
+
d
=
1
2
1
0
© examsnet.com
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