Question

Using the fundamental theorem of algebra, determine the total number of roots of the polynomial function f(x) = (x - 1)(x - 3)(x - 4)?

Answer 1

The polynomial function has 3 complex roots.

Step-by-step explanation:

The given polynomial function is f(x) = (x - 1)(x - 3)(x - 4). Using the fundamental theorem of algebra, we can determine the total number of roots.

The fundamental theorem of algebra states that a polynomial equation of degree 'n' has exactly 'n' complex roots (counting multiplicities).

In this case, the polynomial equation has degree 3, so it will have 3 complex roots. Therefore, the total number of roots of the polynomial function f(x) = (x - 1)(x - 3)(x - 4) is 3.