Degree 3; zeros: 0, 4-i

Question

i just need help with this for my homework

 

Answer 1

You did not state a question, but I assume you want a polynomial of degree 3 with REAL coefficients and the indicated zeros.  For the coefficients to be real, the complex conjugate of any complex zero must also be a zero.  Therefore the zeros are

 

0

4 - i

4 + i

 

The polynomial is

 

p(x) = A(x - 0)[x - (4 - i)][x - (4 + i)]

 

where A is real and A ≠ 0.  You can expand to standard form if you wish.  All of the coefficients will be real.