According to the fundamental theorem of algebra, how many zeros does the function f (x) = 4x3 - x2 - 2x + 1 have?

A) 1

B) 2

C) 3

D) 4

Hello from MrBillDoesMath!

Answer C) (or 3)

Discussion: f (x) is an equation of degree 3 as the highest exponent of "x" is the number 3. The fundamental theorem tell us there are 3 zeroes or roots but not about their character (e. g. are they all real? real and complex?)

Regards, MrB.

Answer: c) 3 roots

Step-by-step explanation:

According to the fundamental theorem of algebra, any polynomial expression of degree n has n roots.

So, in this case:

f (x) = 4x3 - x2 - 2x + 1

The degree of the polynomial expression is given by the highest exponent on a variable. The term that has the highest exponent is 4x∧3.

Since the degree of the polynomial is 3, it has 3 roots.