Question

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

Answer 1

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 2

Answer: c)3 roots

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.