MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2019 LIMIT
2019 LIMIT Category B
Problem 5
inequality with parameter
inequality with parameter
Source: LIMIT 2019 CBS1 P5
April 28, 2021
inequalities
parameterization
Problem Statement
The set of values of
m
m
m
for which
m
x
2
−
6
m
x
+
5
m
+
1
>
0
mx^2-6mx+5m+1>0
m
x
2
−
6
m
x
+
5
m
+
1
>
0
for all real
x
x
x
is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
m
<
1
4
<span class='latex-bold'>(A)</span>~m<\frac14
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
m
<
4
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
m
≥
0
<span class='latex-bold'>(B)</span>~m\ge0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
m
≥
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
0
≤
m
≤
1
4
<span class='latex-bold'>(C)</span>~0\le m\le\frac14
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
0
≤
m
≤
4
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
0
≤
m
<
1
4
<span class='latex-bold'>(D)</span>~0\le m<\frac14
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
0
≤
m
<
4
1
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