Question

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

Answer 1

The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) has exactly \( n \) roots (counting multiplicities and including complex roots).

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

Therefore, according to the Fundamental Theorem of Algebra, the polynomial \( g(x) \) will have exactly 6 roots in the complex number system.