The of
states that if f(x) is a polynomial function of degree n (n> 0), then f has at least one zero in the complex number system.
Let's start by recalling two existence theorems we learned in this chapter. Existence theorems tell us about the existence of the zeros or factors of a polynomial function.
The Fundamental Theorem of Algebra
Linear Factorization Theorem
If f(x) is a polynomial of degree n, where n > 0, then f has at least one zero in the complex number system.
If f(x) is a polynomial of degree n, where n > 0, then f has precisely n linear factors
f(x) = a (x - c_1)(x - c_2)...(x - c_n)
where c_1, c_2, ..., c_n are complex numbers.
We can see that the given sentence matches the content of the Fundamental Theorem of Algebra. With this in mind, let's complete the sentence.
The Fundamental Theorem of Algebra
states that if f(x) is a polynomial function of degree n (n> 0), then f has at least one zero in the complex number system.
