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Byju's Answer
Standard XII
Mathematics
Determinant
If α , β ar...
Question
If
α
,
β
are roots of
a
x
2
+
b
x
+
c
=
0
,
then find the
lim
x
→
α
(
1
+
a
x
2
+
b
x
+
c
)
1
x
−
α
is
Open in App
Solution
x
−
α
⇌
0
f
o
r
a
x
2
+
b
x
+
c
=
0
&
1
+
a
x
2
+
b
x
+
c
=
0
+
1
=
1
∴
lim
x
→
α
(
1
+
a
x
2
+
b
x
+
c
)
1
x
−
α
= y
log y =
1
x
−
α
log (1+ax^{2} + bx + c )$
0
0
∴
L
′
H
o
s
p
i
t
a
l
−
log y =
(
2
a
x
+
b
)
1
+
a
x
2
+
b
x
+
c
1
=
2
a
α
+
b
y
=
e
2
a
α
+
b
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0
Similar questions
Q.
If
α
and
β
be the roots of equation
a
x
2
+
b
x
+
c
=
0
,
then
lim
x
→
α
(
1
+
a
x
2
+
b
x
+
c
)
1
x
−
α
is
Q.
Assertion :
lim
x
→
β
(
1
+
a
x
2
+
b
x
+
c
)
1
x
−
β
is equal to
e
a
(
α
−
β
)
Reason: If
α
,
β
are roots of
a
x
2
+
b
x
+
c
=
0
then
a
x
2
+
b
x
+
c
=
a
(
x
−
α
)
(
x
−
β
)
Q.
If
α
,
β
are roots of
a
x
2
+
b
x
+
c
=
0
and
α
1
,
−
β
are roots of
a
1
x
2
+
b
1
x
+
c
1
=
0
then find the equation whose roots are
α
,
α
1
Q.
If
α
and
β
are the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
,
then
lim
x
→
α
1
−
cos
(
a
x
2
+
b
x
+
c
)
(
x
−
α
)
2
is :
Q.
If
α
,
β
are the roots of
a
x
2
+
b
x
+
c
=
0
,
α
1
,
−
β
are the roots of
a
1
x
2
+
b
1
x
+
c
1
=
0
, show that
α
,
α
1
are the roots of
x
2
b
a
+
b
1
a
1
+
x
+
1
b
c
+
b
1
c
1
=
0
.
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