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UPSC CDS 2 2019 Math Paper
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© examsnet.com
Question : 21
Total: 100
If
(
b
−
6
)
is one root of the quadratic equation
x
2
−
6
x
+
b
=
0
, where b is an integer, then what is the maximum value of
b
2
?
[2019 CDS-II]
36
49
64
81
Validate
Solution:
(
b
−
6
)
is a root of
x
2
−
6
x
+
b
=
0
⇒
(
b
−
6
)
2
−
6
(
b
−
6
)
+
b
=
0
b
2
+
36
−
12
b
−
6
b
+
36
+
b
=
0
b
2
−
17
b
+
72
=
0
b
2
−
9
b
−
8
b
+
72
=
0
b
(
b
−
9
)
−
8
(
b
−
9
)
=
0
(
b
−
8
)
(
b
−
9
)
=
0
⇒
b
=
9
or
b
=
8
Maximum value of
b
2
=
9
2
=
81
© examsnet.com
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