Question

If alpha,beta,gamma are zeros of polynomial p(x),such that alpha+beta+gamma=2,alphabeeta+beta gamma+gamma alpha=-7,alphabeetagamma=-14,then p(x) is?

Answer 1

Answer:

α,β and γ are the zeros of a polynomial

P(x)=ax

3

+bx

2

+cx+d

⟹α⋅β⋅γ=−

a

d

......... (i)

and α+β+γ=

a

c

......... (ii)

Now,

α

1

+

β

1

+

γ

1

=

αβγ

αβ+βγ+γα

=

−d/a

c/a

=−

d

c