ANSWER
4 roots.
EXPLANATION
The given polynomial function is
This is a fourth degree polynomial.
According to the Fundamental Theorem of Algebra, an nth degree polynomial has n roots.
This roots include both real and complex roots.
Also repeated roots or roots with multiplicity greater than one are counted as distinct.
Since the given polynomial function is a fourth degree polynomial, the Fundamental Theorem of Algebra, says that this polynomial has 4 roots.