The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) has exactly \( n \) roots in the complex number system, counted with their multiplicities.
For the polynomial \( g(x) = 7x^6 + 2x - 5 \), the degree \( n \) is \( 6 \) because the highest power of \( x \) is \( x^6 \).
Therefore, according to the Fundamental Theorem of Algebra, the polynomial \( g(x) \) has exactly \( 6 \) roots in the complex number system. These roots may be real or complex, but there will be a total of 6 roots when counting multiplicities.
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