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UPSC NDA 2 2019 Mathematics Solved Paper
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© examsnet.com
Question : 1
Total: 120
If both p and q belong to the set {1, 2, 3, 4}, then how many equations of the form
p
x
2
+
q
x
+
1
=
0
will have real roots?
[NDA II 2019]
12
10
7
6
Validate
Solution:
👈: Video Solution
For
p
x
2
+
q
x
+
1
=
0
to have real roots we must have
q
2
–
4
p
≥
0
⇒
q
2
≥
4
p
If
p
=
1
then
q
2
≥
4
⇒
q
=
2
,
3
,
4
If
p
=
2
then
q
2
≥
8
⇒
q
=
3
,
4
If
p
=
3
then
q
2
≥
12
⇒
q
=
4
If
p
=
4
then
q
2
≥
16
⇒
q
=
4
Thus the number of equations of the form
p
x
2
+
q
x
+
1
=
0
which have real root is 7.
© examsnet.com
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