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Byju's Answer
Standard XII
Mathematics
Methods of Solving a Quadratic Equation
For y=ax2+bx+...
Question
For
y
=
a
x
2
+
b
x
+
c
,
a
>
0
and
α
,
β
be the roots of
a
x
2
+
b
x
+
c
=
0
such that
α
<
β
.
Then
y
<
0
for all
x
∈
A
(
α
,
β
)
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B
(
β
,
∞
)
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C
(
−
∞
,
α
)
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Solution
The correct option is
A
(
α
,
β
)
Given
y
=
a
x
2
+
b
x
+
c
,
a
>
0
And
α
,
β
are the two roots of the equation.
So, we can visualize the graph as shown:
Now, from the graph we can observe that between
α
&
β
,
y
<
0
y
<
0
⇒
x
∈
(
α
,
β
)
Suggest Corrections
0
Similar questions
Q.
If
α
,
β
are the roots of
a
x
2
+
b
x
+
c
=
0
,
(
a
≠
0
)
and
α
+
δ
,
β
+
δ
are the roots of the equation
A
x
2
+
B
x
+
C
=
0
,
(
A
≠
0
)
for the same constant
δ
, then
Q.
If roots of the equation
f
(
x
+
2
)
=
a
x
2
+
b
x
+
c
=
0
and
α
,
β
are such that
α
<
−
2
<
β
, then for the equation
f
(
x
)
=
A
x
2
+
B
x
+
C
.
Q.
For any quadratic equation
y
=
a
x
2
+
b
x
+
c
,
with roots as
α
,
β
such that
α
<
β
if
a
<
0
&
D
>
0
,
then select the correct statements.
Q.
For
y
=
a
x
2
+
b
x
+
c
,
a
>
0
and
α
,
β
be the roots of
a
x
2
+
b
x
+
c
=
0
.
Then
y
>
0
for all
x
∈
(
α
,
β
)
Q.
Let
α
&
β
be the roots of the equation,
a
x
2
+
b
x
+
c
=
0
where
1
<
α
<
β
, then
lim
x
→
m
|
a
x
2
+
b
x
+
c
|
a
x
2
+
b
x
+
c
=
1
, then which of the following is correct?
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