9. 1f α,β, γ are zeroes of polynomial 4x3 - 2x2 + 7, find a) γ + β+α b) αβ + βγ + γα c) αβγ
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Answer:
6x
3
+3x
2
−5x+1=0
Here,
a=6
b=3
c=−5
d=1
∵α,β,γ are zeroes of given polynomial.
∴α+β+γ=
a
−b
=
6
−3
=
2
−1
α.β.γ=
a
−d
=
6
−1
αβ+βγ+γα=
a
c
=
6
−5
∴α
−1
+β
−1
+γ
−1
=
α
1
+
β
1
+
γ
1
⇒=
αβγ
βγ+αγ+βγ
⇒=
(
a
−d
)
(
a
c
)
⇒=
(
6
−1
)
(
6
−5
)
⇒=5
∴α
−1
+β
−1
+γ
−1
=5
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