Answer:
∴f(x) [tex]=x^3-7x^2+9x-63[/tex]
Step-by-step explanation:
Given that, a polynomial of real coefficient with degree 3.
x= -7 and x= -3i are two zeros of the given polynomial.
Conjugate Root Theorem:
The conjugate root theorem state that, if the complex number a+bi is a zero of a polynomial f(x) with real coefficient in one variable, then the complex conjugate a-bi is also a zero of that polynomial.
∴f(x)
= {x-(-7)}(x-3i){x-(-3i)}
=(x-7)(x-3i)(x+3i)
=(x-7){x²-(3i)²}
=(x-7)(x²-9i²)
=(x-7)(x²+9)
[tex]=x^3-7x^2+9x-63[/tex]
∴f(x) [tex]=x^3-7x^2+9x-63[/tex]
