Question

The graph of the function p(x)=x^3+x^2+4x+4 is shown below

Find all real and complex roots of the function. The Zeros are:



List the zeros as complex numbers. Separate answers by commas as needed.

Answer 1

1 ; -2·i ; 2·i

Because x = -1 is a real root, you can divide

(x^3 + x^2 + 4·x + 4)/(x + 1) = x^2 + 4

Roots of x^2 + 4 are

x^2 + 4 = 0

x^2 = -4

x = ± 2·i

All real and complex roots are

1 ; -2·i ; 2·i