if alpha beta and gamma are the zeroes of the polynomial x^3-3x^2+3x^2-1 verify that alpha =beta=gamma
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>Relationship between Zeroes and Coefficients of a Polynomial
>If alpha ,beta ,gamma are ...
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If α,β,γ are the zeroes of the cubic polynomial x
3
+3x
2
−x−2, find the values of the expressions given below:
α+β+γ,αβ+βγ+γα and αβγ.
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x
3
+3x
2
−x−2
The expression is in the from
ax
3
+bx
2
+cx+d,
then
a=1,b=3,c=−1,d=−2
∴α+β+γ=
a
−b
=
1
−3
=−3
αβ+βγ+γα=
a
c
=
1
−1
=−1
αβγ=
a
−d
=
1
−(−2)
=2
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