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Byju's Answer
Standard XIII
Mathematics
Location of Roots
The least pos...
Question
The least positive integral value of
m
for which the equation
x
2
−
2
(
m
−
1
)
x
+
2
m
+
1
=
0
has both roots positive is
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Solution
x
2
−
2
(
m
−
1
)
x
+
2
m
+
1
=
0
Since, both roots are positive, then required condions are
(
i
)
D
≥
0
⇒
(
m
−
1
)
2
−
(
2
m
+
1
)
≥
0
⇒
m
∈
(
−
∞
,
0
]
∪
[
4
,
∞
)
(
i
i
)
−
b
a
>
0
⇒
m
>
1
(
i
i
i
)
c
a
>
0
⇒
m
>
−
1
2
(
i
)
∩
(
i
i
)
∩
(
i
i
i
)
⇒
m
≥
4
So, least positive integer is
4.
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2
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Location of Roots
Standard XIII Mathematics
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