Answer:
Step-by-step explanation:
<u>Given information</u>:
- Polynomial function with real coefficients.
- Zeros: 0, 2i and (3+i).
For any complex number , the complex conjugate of the number is defined as
.
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if f(x) is a polynomial with real coefficients, and 2i is a root of f(x)=0, then its complex conjugate -2i is also a root of f(x)=0.
Similarly, if (3+i) is a root of f(x)=0, then its complex conjugate (3-i) is also a root of f(x)=0.
Therefore, the polynomial in factored form is:
As we have not been given a leading coefficient, assume a = 1:
Expand the polynomial: