Question

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​

Answer 1

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