Question

State how many imaginary and real zeros the function has.

f(x) = x3 + 5x2 + x + 5

0 imaginary; 3 real

1 imaginary; 2 real

3 imaginary; 0 real

2 imaginary; 1 real

Answer 1

it cannot have one imaginary or 3 imaginary since they come in pairs
so it has either 2 imaginary or none

Answer 2

if you want to know if it has one real and two imaginary or three real, graph it

Answer 3

http://www.wolframalpha.com/input/?i=+x3+%2B+5x2+%2B+x+%2B+5
looks like this is actually
\[(x+5)(x^2+1)\] so one real, namely \(-5\) and two imaginary \(i,-i\)

Answer 4

thank you @satellite73