# How do you write a polynomial with zeros -2, -2, 3, -4i and leading coefficient 1?

##### 1 Answer

Mar 31, 2017

# (x+2)^2(x-3)(x^2+16) #

#### Explanation:

We want the following roots:

# -2, -2, 3, -4i #

Complex roots appear in conjugate pairs so the complex root

# -2, -2, 3, 4i, -4i #

By the factor theorem if

For the roots

# (x+2)(x+2) = (x+2)^2#

For the root

# (x-3) #

For the roots

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

Combining these results we get:

# f(x) = (x+2)^2(x-3)(x^2+16) #