Question

Write the polynomial f(x) that meets the given conditions.

Degree 3 polynomial with zeros of -2,4i, and -4i.

Answer 1

f(x) = x^3 + 2 x^2 + 16 x + 32

or also

f(x) = k (x^3 + 2 x^2 + 16 x + 32)

Explanation:

Given that -2, 4i and - 4i are roots, then the binomial factors to be included are:

(x - - 2) (x - 4i) (x --4i) = (x + 2) (x - 4i) (x + 4i) =

(x + 2 ) (x^2 - x 4i + x 4i - 16 i^2) = (x + 2) (x^2 + 16) =

x^3 + 16 x + 2 x^2 + 32

which in standard form reads:

x^3 + 2 x^2 + 16 x + 32

Also have in mind that the polynomial could also include a constant multiplicative factor "k".