State how many imaginary and real zeros the function has.

f(x) = x^4 + 12 x^3 + 37x^2 + 12x + 36

Two real roots and two imaginary roots.

Step-by-step explanation:

Given : Function  

To find : State how many imaginary and real zeros the function has?

Solution :  

Function

We factor the given function,

The factors of the function is equating the function to zero to find roots.

As the number of roots are 4 because of 4 degree polynomial.

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

Therefore, Two real roots and two imaginary roots.