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NIMCET 2008 Question Paper with solutions
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© examsnet.com
Question : 7
Total: 120
If a, b are the roots of
x
2
+
p
x
+
1
=
0
and
c
,
d
are roots of
x
2
+
q
x
+
1
=
0
the value of
E
=
(
a
−
c
)
(
b
−
c
)
(
a
+
d
)
(
b
+
d
)
is
p
2
−
q
2
q
2
−
p
2
q
2
+
p
2
None of these
Validate
Solution:
a. b are roots of
x
2
+
p
x
+
1
=
0
⇒
a
+
b
=
−
p
;
a
b
=
1
...(i)
Also, c and d are roots of
x
2
+
q
x
+
1
=
0
⇒
c
+
d
=
−
q
;
c
d
=
1
.....(ii)
Now,
E
=
(
a
−
c
)
(
b
−
a
)
(
a
+
d
)
(
b
+
d
)
=
(
a
−
c
)
(
b
+
d
)
(
b
−
c
)
(
a
+
c
)
=
(
a
b
−
c
d
−
b
c
+
a
d
)
(
a
b
−
a
c
+
b
d
−
c
d
)
(
∵
a
b
=
c
d
)
=
(
a
d
−
b
c
)
(
b
d
−
a
c
)
=
a
b
(
d
2
+
c
2
)
−
c
d
(
a
2
+
b
2
)
=
a
b
{
(
c
+
d
)
2
−
2
c
d
}
−
c
d
{
(
a
+
b
)
2
−
2
a
b
}
=
(
q
2
−
2
)
−
(
p
2
−
2
)
=
q
2
−
p
2
© examsnet.com
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