N=4; i and 5i are zeroes f(-2)=145

Question

Find the nth degree polynomial

Answer 1

f(x) = a(x - i)(x + i)(x - 5i)(x + 5i)

f(x) = a(x² + 1)(x² + 5)

f(x) = a(x⁴ + 6x² + 5)

145 = a((-2)⁴ + 6(-2)² + 5)

You determine a.