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Byju's Answer
Standard XII
Mathematics
Greatest Integer Function
If b2<4ac t...
Question
If
b
2
<
4
a
c
then roots of equation
a
x
4
+
b
x
2
+
c
=
0
are real and distinct if:
A
b
<
0
,
a
<
0
,
c
>
0
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B
b
<
0
,
a
>
0
,
c
>
0
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C
b
>
0
,
a
>
0
,
c
>
0
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D
b
>
0
,
a
<
0
,
c
<
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
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Solution
The correct options are
B
b
<
0
,
a
>
0
,
c
>
0
D
b
>
0
,
a
<
0
,
c
<
0
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0
Similar questions
Q.
The roots of
a
x
2
+
b
x
+
c
=
0
,
a
≠
0
are real and unequal, if
(
b
2
-
4
a
c
)
(a) > 0
(b) = 0
(c) < 0
(d) none of these
Q.
Assertion :
Consider the function
f
(
x
)
=
log
c
(
a
x
3
+
(
a
+
b
)
x
2
+
(
b
+
c
)
x
+
c
)
.
Domain of the functions is
(
−
1
,
∞
)
∼
{
−
(
b
/
2
a
)
}
,
where
a
>
0
,
b
2
−
4
a
c
=
0
Reason:
Consider the function
f
(
x
)
=
log
c
(
a
x
3
+
(
a
+
b
)
x
2
+
(
b
+
c
)
x
+
c
)
.
a
x
2
+
b
x
+
c
=
0
has equal roots when
b
2
−
4
a
c
=
0
Q.
Assertion :If
a
+
b
+
c
>
0
,
a
<
0
<
b
<
c
, then roots of the equation
a
(
x
−
b
)
(
x
−
c
)
+
b
(
x
−
c
)
(
x
−
a
)
+
c
(
x
−
a
)
(
x
−
b
)
=
0
are real. Reason: Roots of the equation
A
x
2
+
B
x
+
K
=
0
are real if
B
2
−
4
A
K
>
0
.
Q.
If
b
2
≥
4
a
c
for the equation
a
x
4
+
b
x
2
+
c
=
0
, then all roots of the equation will be real if
Q.
If the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
are opposite in sign and positive root is greater in magnitude, then
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