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Quantitative Aptitude
Quadratic Equations
If p, q, r ar...
Question
If p, q, r are real, then roots of the equation
x
2
−
2
p
x
+
p
2
−
q
2
−
r
2
=
0
will always be?
A
Real
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B
Imaginary
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C
Equal
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D
None of these
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Solution
The correct option is
A
Real
Option (a) is the correct answer. Check the video for the approach.
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1
Similar questions
Q.
Show that the roots of the equation
x
2
−
2
p
x
+
p
2
−
q
2
+
2
q
r
−
r
2
=
0
are rational.
Q.
If
(
p
2
−
q
2
)
x
2
+
(
q
2
−
r
2
)
x
+
r
2
−
p
2
=
0
and
(
p
2
−
q
2
)
y
2
+
(
r
2
−
p
2
)
y
+
q
2
−
r
2
=
0
have a common root for all real values of p, q and r, then find the common root.
Q.
Assertion :If
s
e
c
α
,
c
o
s
e
c
α
are the roots of the equation
x
2
−
p
x
+
q
=
0
, then
p
2
−
2
q
−
q
2
=
0
. Reason: If p, q are the roots of the equation
x
2
−
x
s
i
n
α
+
c
o
s
α
=
0
, then
p
2
=
1
−
q
2
1
+
q
2
.
Q.
Let
p
,
q
a
n
d
r
be real numbers
(
p
≠
q
,
r
≠
0
)
, such that the roots of the equation
1
x
+
p
+
1
x
+
q
=
1
r
are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to :
Q.
Given that the equation
z
2
+
(
p
+
i
q
)
z
+
r
+
i
s
=
0
where p,q,r,s are real and non-zero has a real root, then
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