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Byju's Answer
Standard XII
Mathematics
Geometrical Representation of a Complex Number
All the three...
Question
All the three roots of
a
z
3
+
b
z
3
+
c
z
+
d
=
0
have negative real parts
(
a
,
b
,
c
∈
R
)
, then
A
a
b
>
0
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B
b
c
>
0
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C
a
d
>
0
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D
A
l
l
o
f
t
h
e
s
e
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Solution
The correct option is
A
a
b
>
0
The problem is negative find the condition that all roots of ,
f
(
z
)
=
a
z
3
+
b
z
2
+
c
z
+
d
=
0
f
'
(
z
)
=
3
a
z
2
+
2
b
z
+
c
z
=
−
2
b
±
−
√
(
4
b
2
−
12
a
c
)
6
a
Therefore,
−
2
b
6
a
<
0
a
b
>
0
.
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0
Similar questions
Q.
If
x
2
−
(
a
+
b
+
c
)
x
+
(
a
b
+
b
c
+
c
a
)
=
0
has non real roots, where
a
,
b
,
c
∈
R
+
, then
√
a
,
√
b
,
√
c
Q.
Let a > 0, b > 0 and c > 0. Then both the roots of the equation
2
a
x
2
+
3
b
x
+
5
c
=
0
Q.
If both the roots of
a
x
2
+
b
x
+
c
=
0
are real, positive and distinct, then
(where
Δ
=
b
2
−
4
a
x
)
Q.
For the quadratic equation
a
x
2
+
b
x
+
c
=
0
;
a
,
b
,
c
∈
R
,
which of the following is/are true ? (where
Δ
=
b
2
−
4
a
c
,)
Q.
Statement 1 : If
f
(
x
)
=
a
x
2
+
b
x
+
c
, where
a
>
0
,
c
<
0
and
b
∈
R
, then roots of
f
(
x
)
=
0
must be real and distinct .
Statement 2 : If
f
(
x
)
=
a
x
2
+
b
x
+
c
,
where
a
>
0
,
b
∈
R
,
b
≠
0
and the roots of
f
(
x
)
=
0
are real and distinct, then
c
is necessarily negative real number .
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