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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
.
Then
y
>
0
for all
x
∈
(
α
,
β
)
A
True
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B
False
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Solution
The correct option is
B
False
Suggest Corrections
0
Similar questions
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
such that
α
<
β
.
Then
y
<
0
for all
x
∈
Q.
If alpha, beta are roots of ax2 + bx + c = 0, then the equation ax2 - bx (x - 1) + c(x - 1)2 = 0 has roots 1) alpha/(1-alpha), beta/(1-beta) 2) (1- alpha)/alpha, (1-beta)/beta 3) alpha/(1+alpha), beta/(1+beta) 4) (1+alpha)/alpha, (1+beta)/beta
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
a
,
b
,
c
are real numbers and
a
≠
0.
If
α
is a root of
a
2
x
2
+
b
x
+
c
=
0
and
β
is a root of
a
2
x
2
−
b
x
−
c
=
0
such that
0
<
α
<
β
, then the equation
a
2
x
2
+
2
b
x
+
2
c
=
0
has a root
γ
that always satisfies
Q.
a
x
2
+
b
x
+
c
=
0
has real and distinct roots
α
and
β
(
β
>
α
)
. Further
a
>
0
,
b
<
0
and
c
<
0
, then
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