Question

State how many imaginary and real zeros the function has.

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

Answer 1

\[f(x) = x^3+5x^2+x+5\] can be rewritten as: \[f(x) = (x+5)(x^2+1)\] So the real zeros are: \[-5\] and imaginary ones are given by: \[x^2+1 = 0\]\[x^2 = -1\]\[x = +i\]or \[x = -i\]