Form a polynomial function f(x) of degree 4, with a leading coefficient of 1, and contains the zeros 7,-7,and 2i

Question

a) write the function f(x) in factored form

b) multiply and simplify the function f(x)

Answer 1

(a)

The complex conjugate of a complex zero must also be a zero, so the 4 zeros are

7

-7

2i

-2i

f(x) = 1(x - 7)(x + 7)(x - 2i)(x + 2i)

(b)

I will get you started.

(x - 7)(x + 7) = x² - 49

(x - 2i)(x + 2i) = x² + 4

f(x) = (x² - 49)(x² + 4)

You finish from here.