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Manipal Entrance Test 2016 Math Paper
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© examsnet.com
Question : 1
Total: 70
If
2
a
+
3
b
+
6
c
=
0
,
then atleast one root of the equation
a
x
2
+
b
x
+
c
=
0
lies in the interval
(
0
,
1
)
(
1
,
2
)
(
2
,
3
)
None of these
Validate
Solution:
Consider the function
f
(
x
)
=
a
x
3
3
+
b
x
2
2
+
c
x
+
d
We have,
f
(
0
)
=
d
and
f
(
1
)
=
a
3
+
b
2
+
c
+
d
=
2
a
+
3
b
+
6
c
6
+
d
=
0
6
+
d
[
∵
2
a
+
3
b
+
6
c
=
0
]
Therefore, 0 and 1 are roots of the polynomial
f
(
x
)
.
Hence, according to Rolle's theorem, there exists atleast one root of the polynomial
f
′
(
x
)
=
a
x
2
+
b
x
+
c
lying between 0 and 1.
© examsnet.com
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