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KEAM 2018 Math Paper
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© examsnet.com
Question : 38
Total: 120
A quadratic equation
a
x
2
+
b
x
+
c
=
0
,
with distinct coefficients is formed. If a, b, c are chosen from the numbers 2, 3, 5, then the probability that the equation has real roots is
1
3
2
5
1
4
1
5
2
3
Validate
Solution:
Total number of ways of assigning values 2,3 , 5 to
a
,
b
,
c
,
=
3
!
=
6
Now, for quadratic equation
a
x
2
+
b
x
+
c
=
0
to have real roots
b
2
−
4
a
c
≥
0
.
This is possible only
when
a
=
2
,
b
=
5
,
c
=
3
or
a
=
3
,
b
=
5
,
c
=
2
⇒
Required probability
=
2
6
=
1
3
© examsnet.com
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