how to find a 3rd degree polynomial with zeros as 3 and -5i.

Answer 1

If the coefficients are real, the complex conjugate of any complex zero must also be a zero. Therefore your 3 zeros are

3

-5i

5i

p(x) = A(x - 3)(x + 5i)(x - 5i) = A(x - 3)(x² + 25)

where A is real and A ≠ 0.