Find an end degree polynomial function with the real coefficient satisfying the given condition

Question

N=3; 5, -3i, f(2)=195

Find an nth degree polynomial function with real coefficient satisfying the given condition

Answer 1

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

5

-3i

3i

f(x) = A(x - 5)(x + 3i)(x - 3i)

f(x) = A(x - 5)(x² + 9),

where A is real and A ≠ 0.

Solve for A by plugging in x=2.

f(2) = 195 = A(2 - 5)(2² + 9)

Solve for A and finish from here.