if alpha beta and gamma are the zeros of cubic polynomial x cube minus 3 x square - 3 x + b is equal to zero between the coefficient and zero
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2
Answer:
Ggiven that
p(x)=ax
3
+bx
2
+cx+d .........(1) where a
=0 is a cubic polynomial
And α,β,γ are the zeroes of the polynomial p(x)
We can also write the polynomial in this way
p(x)=(x−α)(x−β)(x−γ)
⇒p(x)=x
3
−(α+β+γ)x
2
+(αβ+βγ+γα)x−αβγ .............(2)
Equations (1) and (2) are same
Comparing the coefficients
1
a
=
−α−β−γ
b
=
αβ+βγ+γα
c
=
−αβγ
d
On solving we get the following results
α+β+γ=
a
−b
= Sum of the roots
αβ+βγ+γα=
a
c
αβγ=
a
−d
= product of roots
Hence, option D is correct
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