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UPSC NDA Math Model Paper 9
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© examsnet.com
Question : 11
Total: 120
If
α
,
β
are the roots of the equation
3
x
2
+
57
x
−
5
=
0
, then what is
a
3
+
β
3
a
−
3
+
β
−
3
equal to ?
- 27/125
81/125
27/125
-125/27
Validate
Solution:
Given quadratic equation:
3
x
2
+
57
x
−
5
=
0
Let
α
and
β
are roots, then
α
+
β
=
−
57
∕
3
,
α
β
=
−
5
∕
3
Now,
α
3
+
β
3
α
−
3
+
β
−
3
=
α
3
+
β
3
1
a
3
+
1
β
3
=
α
3
+
β
3
(
a
3
+
β
3
)
a
3
β
3
=
(
α
β
)
3
=
(
−
5
∕
3
)
3
=
−
125
∕
27
Hence, option (4) is correct.
© examsnet.com
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