Question

Write a polynomial fx that satisfies the given conditions. Express the polynomial with the lowest possible leading positive integer coefficient. Polynomial of lowest degree with lowest possible integer coefficients and zeros of 6i and −2i.

Answer 1

 

f(x) = (x - 6i)(x - (-2i))

f(x) = (x - 6i)(x + 2i)

f(x) = x² - 6xi + 2xi  - 12i²     (but i² = -1)

f(x) = x² - 6xi + 2xi  + 12

f(x) = x² - 4xi + 12