find a polynomial function with real coefficients that has the given zeros, 1, 5i

Answer 1

Zeros containing complex numbers exist only as pairs that are conjugates of each other.

-5i = 0 - 5i, whose conjugate is: 0 - 5i = -5i

Factors are therefore:

(x – 1), (x - 5i), and (x + 5i)

Polynomial function is then:

f(x) = (x – 1)(x - 5i)(x + 5i)

f(x) = (x – 1)(x² +25)

f(x) = x³ – x² + 25x - 25