Question

How many roots, including complex roots, does the function represented by the polynomial

4z3+3z + 3 have?
A) 4
B) 2
C) 1

Answer 1

The polynomial
`4z^3 + 3z + 3` has 3 roots, including real and complex roots, according to the Fundamental Theorem of Algebra.

Step-by-step explanation:

The polynomial given is
`4z^3 + 3z + 3`. According to the Fundamental Theorem of Algebra, every non-constant single-variable polynomial with complex coefficients has as many complex roots as its degree, counting each root up to its multiplicity. Thus, the cubic polynomial given would have 3 roots, including real roots and complex roots (if any).