Find an nth-degree polynomial with real coefficients and satisfying the given conditions.

Question

N=3

-3 and 9+2i are zeros

f(1)=272

Answer 1

Complex roots are always in conjugate pairs:

f(x) = a(x - 3)(x - (9 + 2i))(x - (9 - 2i))

f(x) = a(x - 3)(x + 85)

f(x) = a(x² + 82x - 255)

272 = a(1 + 82 - 255)

Can you determine a and answer>