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Byju's Answer
Standard XI
Mathematics
Proof by mathematical induction
If a, b are...
Question
If
a
,
b
are the roots of
x
2
+
p
x
+
1
=
0
and
c
,
d
are the roots of
x
2
+
q
x
+
1
=
0
. Then
(
a
−
c
)
(
b
−
c
)
(
a
+
d
)
(
b
+
d
)
(
q
2
−
p
2
)
=
.
Open in App
Solution
x
2
+
p
x
+
1
=
0
a
+
b
=
−
p
a
b
=
1
x
2
+
q
x
+
1
=
0
c
+
d
=
−
q
c
d
=
1
(
a
−
c
)
(
b
−
c
)
=
a
b
−
(
a
+
b
)
c
+
c
2
(
1
+
p
c
+
c
2
)
(
a
+
d
)
(
b
+
d
)
=
a
b
+
(
a
+
b
)
d
+
d
2
=
(
1
−
p
d
+
d
2
)
∴
(
1
+
p
c
+
c
2
)
(
1
−
p
d
+
d
2
)
=
1
−
p
d
+
d
2
+
p
c
−
p
2
c
d
+
c
2
−
p
c
2
d
+
c
2
d
2
=
1
+
c
2
+
d
2
+
p
c
−
p
c
2
d
+
p
c
d
2
−
p
d
+
p
2
c
d
+
c
2
d
2
=
1
+
c
2
+
d
2
+
p
c
−
p
c
+
p
d
−
p
d
+
p
2
+
1
=
2
+
p
2
+
(
c
+
d
)
2
−
2
d
=
2
+
p
2
+
q
2
−
2
=
p
2
+
q
2
∴
(
a
−
c
)
(
b
−
c
)
(
a
+
d
)
(
b
+
d
)
q
2
−
p
2
=
q
2
+
p
2
q
2
−
p
2
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0
Similar questions
Q.
If a and b are the roots of the equation x
2
+px+1=0 and ; c and d are the roots of the equation x
2
+qx+1=0, then (a-c)(b-c)(a+d)(b+d)=?
Q.
If
a
,
b
are the roots of the equation
x
2
+
p
x
+
1
=
0
and
c
,
d
are the roots of the equation
x
2
+
q
x
+
1
=
0
,
then
(
a
−
c
)
(
b
−
c
)
(
a
+
d
)
(
b
+
d
)
=
Q.
If
a
,
b
are the real roots of
x
2
+
p
x
+
1
=
0
and
c
,
d
are the real roots of
x
2
+
q
x
+
1
=
0
, then
(
a
−
c
)
(
b
−
c
)
(
a
+
d
)
(
b
+
d
)
is divisible by
Q.
If
a
and
b
are the roots of equation
x
2
+ px + 1 = 0
and
c,
d are the roots of equation
x
2
+ qx + 1 = 0
, then the value of
E =
(
a - c
)
(
b - c
)
(
a + d
)
(
b + d
)
is
Q.
If a and b are the roots of the equation
x
2
+
p
x
+
1
=
0
and c and d are the roots of the equation
x
2
+
q
x
+
1
=
0
,then
(
a
−
c
)
(
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c
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(
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)
(
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