Apply the Fundamental Theorem of Algebra to find the number of roots for the polynomial g(x) = 7x^6+2x-5
The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots, counting multiplicity.
In this case, the polynomial g(x) = 7x^6 + 2x - 5 is of degree 6. Therefore, it has exactly 6 roots, counting multiplicity.
To apply the Fundamental Theorem of Algebra and determine the number of roots for the polynomial g(x) = 7x^6 + 2x - 5, we need to consider the degree of the polynomial.
The degree of a polynomial is the highest power of x in the polynomial. In this case, g(x) has a degree of 6 because the highest power of x is 6.
According to the Fundamental Theorem of Algebra, a polynomial of degree n can have at most n roots, counting multiplicity. This means that the polynomial g(x) can have at most 6 roots.
However, it does not guarantee that g(x) will have exactly 6 roots. The number of roots can be less than 6 or equal to 6 depending on the specific factors of the polynomial.
To determine the exact number of roots and their nature (real or complex), we would need to use additional techniques such as factoring, the rational root theorem, or graphing the polynomial.
To find the number of roots of a polynomial using the Fundamental Theorem of Algebra, we need to look at the degree of the polynomial. The degree of a polynomial is the highest power of the variable in the polynomial.
In this case, the polynomial g(x) = 7x^6 + 2x - 5 has a degree of 6, which means it is a sixth-degree polynomial.
According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex roots, counting multiplicity.
Therefore, the polynomial g(x) = 7x^6 + 2x - 5 will have exactly 6 complex roots, counting multiplicity.
Please note that these roots can be real or complex numbers. To determine their exact values, you would need to use numerical methods or factorization techniques.