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UPSC NDA Math Model Paper 1
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© examsnet.com
Question : 51
Total: 120
If the roots of the equation
a
x
2
−
2
b
x
+
c
=
0
are
n
and
m
, then the value of
b
a
n
2
+
c
+
b
a
m
2
+
c
is:
c
a
b
a
a
c
b
c
Validate
Solution:
Given:
a
x
2
−
2
b
x
+
c
=
0
Using the formula for the sum and the product of the roots we get:
m
+
n
=
2
b
a
.......(1)
m
n
=
c
a
.......(2)
Now, the given expression
b
a
n
2
+
c
+
b
a
m
2
+
c
:
=
2
b
a
2
(
n
2
+
c
a
)
+
2
b
a
2
(
m
2
+
c
a
)
=
m
+
n
2
(
n
2
+
m
n
)
+
m
+
n
2
(
m
2
+
m
n
)
=
m
+
n
2
n
(
n
+
m
)
+
m
+
n
2
m
(
m
+
n
)
=
1
2
(
1
m
+
1
n
)
=
1
2
(
m
+
n
m
n
)
=
1
2
(
2
b
a
c
a
)
=
b
c
.
© examsnet.com
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