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Byju's Answer
Standard XII
Mathematics
Location of Roots when Compared with a constant 'k'
If both roots...
Question
If both roots of
a
x
2
+
b
x
+
c
=
0
,
a
>
0
are greater than
k
then
−
b
2
a
>
k
.
A
False
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B
True
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Solution
The correct option is
B
True
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1
Similar questions
Q.
If both the roots
α
,
β
of the quadratic equation
a
x
2
+
b
x
+
c
=
0
,
a
<
0
are less than a real number
k
such that
k
>
α
>
β
Considering
f
(
x
)
=
a
x
2
+
b
x
+
c
, select the correct statement(s).
Q.
Consider
f
(
x
)
=
a
x
2
+
b
x
+
c
with
a
>
0
,
If both roots of the quadratic equation are greater than any constant
k
. The necessary and sufficient condition for this are :
Q.
If the roots of
a
x
2
+
b
x
+
c
=
0
are
α
,
β
and the roots of
A
X
2
+
B
x
+
C
=
0
are
(
α
−
k
)
,
(
β
−
k
)
.
Then
(
B
2
−
4
A
C
b
2
−
4
a
c
)
is equal to
Q.
If
k
∈
R
lies between the roots of
a
x
2
+
b
x
+
c
=
0
,
a
<
0
. Consider
f
(
x
)
=
a
x
2
+
b
x
+
c
=
0
, then
f
(
k
)
&
Q.
If the roots of
a
x
2
+
b
x
+
c
=
0
are in the ratio
1
:
k
, then
c
k
2
+
b
k
+
c
=
0
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