Question

Apply the Fundamental Theorem of Algebra to find the number of roots for the polynomial g(x)=7x6+2x−5
.(1 point)
roots

Answer 1

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

For the polynomial \( g(x) = 7x^6 + 2x - 5 \), the highest degree term is \( 7x^6 \), which indicates that the polynomial is of degree 6.

Therefore, according to the Fundamental Theorem of Algebra, the polynomial \( g(x) \) has exactly **6 roots** in the complex number system (some of which may be real or may be repeated roots).