N=4, i and 3i are zeros, f(-1)=20 find an nth-degree polynomial function with real coefficients satisfying the given conditions

Answer 1

In order to have real coefficients, the complex conjugates of complex zeros must also be zeros. Therefore, your 4 zeros are

i

-i

3i

-3i

The polynomial is

f(x) = A(x - i)(x + i)(x - 3i)(x + 3i),

where A is real and A ≠ 0.

f(x) = A(x² + 1)(x² + 9)

Now set

f(-1) = 20,

plug in x = -1, evaluate, and get the value of A. You should be able to finish from here.