Question

State how many imaginary and real zeros the function has.

f(x) = x4 + 12 x3 + 37x2 + 12x + 36

Answer 1

2 real roots and 2 imaginary roots

Explanation:

The roots are x=i,-i,-6,-6.

Answer 2

Explanation:

If you'd graph this function on a graphing calculator or graphing utility, you'd see quickly that the graph never touches or crosses the x-axis. This tells us immediately that there are no real roots; all four roots are complex or imaginary.