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Byju's Answer
Standard XII
Mathematics
Composite Function
Let exactly o...
Question
Let exactly one root of the equation ax^2+bx+c=0 lies between (0,1). Then prove that c(a+b+c)<0
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Similar questions
Q.
Which of the following equation has exactly one root as
0
?
(
a
,
b
,
c
>
0
)
Q.
Assertion :If equation
a
x
2
+
b
x
+
c
=
0
and
x
2
−
3
x
+
4
=
0
have exactly one root common, then at least one of
a
,
b
,
c
is imaginary. Reason: If
a
,
b
,
c
are not all real, then equation
a
x
2
+
b
x
+
c
=
0
can have one real root and one one root imaginary.
Q.
'
a
f
(
k
)
<
0
' is the necessary and sufficient condition for a particular real number
k
to lie between the roots of a quadratic equation
f
(
x
)
=
0
, where
f
(
x
)
=
a
x
2
+
b
x
+
c
. If
f
(
k
1
)
f
(
k
2
)
<
0
, then exactly one of the roots will lie between
k
1
and
k
2
.
If
c
(
a
+
b
+
c
)
<
0
<
a
(
a
+
b
+
c
)
, then
Q.
Let
a
>
0
,
b
>
0
,
c
>
0
then both roots of the equation
a
x
2
+
b
x
+
c
=
0
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
)
&
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