if alpha, beta, gamma are the roots if x^3+ax^2+bc+c=0 then sigma(alpha+beta-gamma)=
it's important please answer correctly
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Step-by-step explanation:
Correct option is
D
c
ab
−3
As α,β,γ are roots of x
3
+ax
2
+bx+c=0, gives
S
1
=α+β+γ=−a
S
2
=αβ+βγ+γα=b
S
3
=αβγ=−c
Now,
∑(
β
α
+
α
β
)=∑(
αβ
α
2
+β
2
)
=
αβ
(α
2
+β
2
)
+
βγ
(β
2
+γ
2
)
+
αγ
(α
2
+γ
2
)
=
αβγ
α
2
γ+β
2
γ+αβ
2
+αγ
2
+α
2
β+βγ
2
=
S
3
S
1
S
2
−3S
3
=
c
ab−3c
=
c
ab
−3
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