How many real and complex roots exists for a polynomial?

Step-by-step explanation:

whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial. as an example, we'll find the roots of the polynomial ...

x^5 - x^4 + x^3 - x^2 - 12x + 12.

the fifth-degree polynomial does indeed have five roots; three real, and two complex.