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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
Let a,b,c be ...
Question
Let a,b,c be real , if
a
x
2
+
b
x
+
c
=
0
has two real roots
α
and
β
, where
α
<
−
1
a
n
d
β
>
1
, then show that
c
a
+
∣
∣
∣
b
a
∣
∣
∣
<
−
y
Find y
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Solution
for
a
x
2
+
b
x
+
c
=
0
α
<
−
1
and
β
>
1
Therefore,
f
(
−
1
)
f
(
1
)
<
0
Therefore,
⇒
(
c
+
b
+
a
)
(
c
−
b
+
a
)
<
0
⇒
c
a
+
∣
∣
∣
b
a
∣
∣
∣
<
−
1
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0
Similar questions
Q.
Let a, b, c be real and
a
x
2
+
b
x
+
c
=
0
has two real roots α and β where
α
<
–
1
a
n
d
β
>
1
, then
1
+
c
a
+
∣
∣
b
a
∣
∣
Q.
If
α
,
β
are roots of the equation
a
x
2
+
b
x
+
c
=
0
, where
a
,
b
,
c
are distinct real values, then
(
1
+
α
+
α
2
)
(
1
+
β
+
β
2
)
is
Q.
If
α
,
β
be unequal real roots of the equation
a
x
2
+
b
x
+
c
=
0
where
a
,
b
,
c
are real and
γ
is the solution of
2
a
x
+
b
=
0
then
Q.
If
α
,
β
are real and distinct roots of
a
x
2
+
b
x
−
c
=
0
and
p
,
q
are real and distinct roots of
a
x
2
+
b
x
−
|
c
|
=
0
, where
(
a
>
0
)
, then
Q.
If
f
(
x
)
=
a
x
2
+
b
x
+
c
,
a
,
b
,
c
∈
R
and equation
f
(
x
)
−
x
=
0
has non-real roots
α
,
β
. Let
γ
,
δ
be the roots of
f
(
f
(
x
)
)
−
x
=
0
(
γ
,
δ
are not equal to
α
,
β
). Then
∣
∣ ∣
∣
2
α
δ
β
0
α
γ
β
1
∣
∣ ∣
∣
is
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