Question

Can someone please help me with this problem ASAP thank you

Answer 1

3-degree polynomial is f(x )=
`[x^(3 )-(9)/(7) x^(2)+9x-(81)/(7) ]`

Explanation:

Given that polynomial f(x) is 3-degree polynomial and Zeros/Roots at x=
`(9)/(7)` and x= -3i

In order to find the equation of a 3-degree polynomial, we need 3 roots.

Here, One of Root is real number x=
`(9)/(7)` and another root is an imaginary number x=(-3i)

It is necessary to note that imaginary roots always come in pair of conjugates

Therefore, Comjugate0 of x =(-3i) is 3rd root

Conjugate of (-3i) is 3i

Evaluting equation of polynomial,

=
`[x-3i][x+3i][x-(9)/(7) ]`

=
`[x^(2)-(3i)^(2)][x-(9)/(7) ]`

=
`[x^(2)-(9)(i)^(2)][x-(9)/(7) ]`

=
`[x^(2)+9][x-(9)/(7) ]`

f(x )=
`[x^(3 )-(9)/(7) x^(2)+9x-(81)/(7) ]`