Question

Can someone please help me with this problem ASAP thank you

Answer 1

3-degree polynomial is f(x )= $[x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ]$

Step-by-step explanation:

Given that polynomial f(x) is 3-degree polynomial and Zeros/Roots at x= $\frac{9}{7}$ 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=$\frac{9}{7}$ 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,

=$[x-3i][x+3i][x-\frac{9}{7} ]$

=$[x^{2}-(3i)^{2}][x-\frac{9}{7} ]$

=$[x^{2}-(9)(i)^{2}][x-\frac{9}{7} ]$

=$[x^{2}+9][x-\frac{9}{7} ]$

f(x )= $[x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ]$