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UPSC 2016 CDS II Math Paper
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© examsnet.com
Question : 14
Total: 100
If α and β are the two zeros of the polynomial
25
x
2
−
15
x
+
2
,
then what is a quadratic polynomial whose zeros are
(
2
α
)
−
1
and
(
2
β
)
−
1
?
[2016 CDS-II]
x
2
+
30
x
+
2
8
x
2
−
30
x
+
25
8
x
2
−
30
x
x
2
+
30
x
Validate
Solution:
α
+
β
=
−
(
−
15
)
25
=
3
5
and
α
β
=
2
25
Sum of roots of the required polynomial
=
1
2
α
+
1
2
β
=
1
2
(
α
+
β
α
β
)
=
1
2
×
3
5
2
25
=
15
4
Product of roots of the required polynomial
=
1
2
α
×
1
2
β
=
1
4
α
β
7
=
1
4
×
2
25
=
25
8
∴ Required quadratic polynomial
=
x
2
– (Sum of the roots) x + Product of the roots
=
x
2
−
15
4
x
+
25
8
=
8
x
2
−
30
x
+
25
© examsnet.com
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