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Byju's Answer
Standard XIII
Mathematics
Nature of Roots
For the equat...
Question
For the equation
x
2
+
b
x
+
c
=
0
,
if
1
+
b
+
c
=
0
for all
b
,
c
∈
R
,
then roots are
A
1
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B
b
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C
c
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D
1
c
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Solution
The correct option is
C
c
If
a
x
2
+
b
x
+
c
=
0
be a quadratic &
a
+
b
+
c
=
0
,
then
x
=
1
is one solution & the other solution will be
c
a
x
2
+
b
x
+
c
=
0
and
1
+
b
+
c
=
0
⇒
x
=
1
&
x
=
c
are two solutions
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0
Similar questions
Q.
For the equation
x
2
+
b
x
+
c
=
0
,
if
1
+
b
+
c
=
0
for all
b
,
c
∈
R
,
then the roots are
Q.
For the equation
x
2
+
b
x
+
c
=
0
,
if
1
+
b
+
c
=
0
for all
b
,
c
∈
R
,
then roots are
Q.
If roots of equation
2
x
2
+
b
x
+
c
=
0
;
b
,
c
∈
R
, are real & distinct then the roots of equation
2
c
x
2
+
(
b
−
4
c
)
x
+
2
c
−
b
+
1
=
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are
Q.
If
r
and
s
are the root of the equation
x
2
+
b
x
+
c
=
0.
where
b
and
c
are constants, is
r
s
<
0
?
(1)
b
<
0
(2)
c
<
0
Q.
Assertion :If the equation
a
x
2
+
b
x
+
c
=
0
,
(
a
,
b
,
c
∈
R
,
a
≠
0
)
and
x
2
+
2
x
+
3
=
0
have a common root , then
a
:
b
:
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is
1
:
2
:
3
. Reason: The roots of the equation
x
2
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x
+
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are imaginary.
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Nature of Roots
Standard XIII Mathematics
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