2. Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and product of its zeros as 3, -1 and - 3 respectively.
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1
Let,
α
,
β
,
γ
be the zeros of the given cubic polynomial. Then, we have
α
+
β
+
γ
=
2
α
β
+
β
γ
+
γ
α
=
−
7
α
β
γ
=
−
14
Now, the required polynomial
=
k
×
[
x
3
−
(
α
+
β
+
γ
)
x
2
+
(
α
β
+
β
γ
+
γ
α
)
x
−
(
α
β
γ
)
]
, where k is real constant.
=
k
×
[
x
3
−
2
x
2
+
(
−
7
)
x
−
(
−
14
)
]
=
k
×
(
x
3
−
2
x
2
−
7
x
+
14
)
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