3-degree polynomial is f(x )= [tex][x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ][/tex]
Step-by-step explanation:
Given that polynomial f(x) is 3-degree polynomial and Zeros/Roots at x= [tex]\frac{9}{7}[/tex] 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=[tex]\frac{9}{7}[/tex] 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,
=[tex][x-3i][x+3i][x-\frac{9}{7} ][/tex]
=[tex][x^{2}-(3i)^{2}][x-\frac{9}{7} ][/tex]
=[tex][x^{2}-(9)(i)^{2}][x-\frac{9}{7} ][/tex]
=[tex][x^{2}+9][x-\frac{9}{7} ][/tex]
f(x )= [tex][x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ][/tex]
