Question

the fundamental theorem of algebra practice
complete this assessment to review what youve learned. it will not count toward your grade.

apply the fundamental theorem of algebra to find the number of roots for the polynomial ( g(x) = 7x^6 + 2x - 5 ).
(1 point)

□ roots

check answer remaining attempts 3

Explanation:

Step1: Recall Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) has exactly \( n \) roots (counting multiplicities) in the complex number system.

Step2: Determine the degree of the polynomial

For the polynomial \( g(x) = 7x^6 + 2x - 5 \), the highest power of \( x \) is 6. So the degree \( n = 6 \).

Step3: Apply the theorem

By the Fundamental Theorem of Algebra, since the degree of \( g(x) \) is 6, the polynomial has 6 roots (in the complex plane, considering multiplicities).

Answer:

6