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KVPY SA Exam 2015 Question Paper
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© examsnet.com
Question : 1
Total: 80
PART I
MATHEMATICS
Two distinct polynomials
f
(
x
)
and
g
(
x
)
are defined as follows:
f
(
x
)
=
x
2
+
a
x
+
2
;
g
(
x
)
=
x
2
+
2
x
+
a
.
If the equations
f
(
x
)
=
0
and
g
(
x
)
=
0
have a common root then the sum of the roots of the equation
f
(
x
)
+
g
(
x
)
=
0
is
−
1
2
0
1
2
1
Validate
Solution:
Let 'α' is the common root
So,
α
2
+
a
α
+
2
=
0
....(i)
α
2
+
2
α
+
a
=
0
...(ii)
⇒
(
a
−
2
)
α
+
2
–
a
=
0
⇒ α = 1 is common root.
∴
1
2
+
a
+
2
=
0
⇒
a
=
−
3.
f(x) + g(x) = 0
⇒
2
x
2
+
(
a
+
2
)
x
+
(
a
+
2
)
=
0
⇒
2
x
2
−
x
−
1
=
0
⇒ Sum of roots =
1
2
.
© examsnet.com
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