according to the fundamental theorem of algebra how many roots does the polynomial function p(x)=5x^2-3x^3+6x^5-4x^4 have

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 \( p(x) = 5x^2 - 3x^3 + 6x^5 - 4x^4 \), we first need to determine its degree. The degree of a polynomial is the highest power of \( x \) in the polynomial.

In this case, the highest power of \( x \) is \( x^5 \). Therefore, the degree of the polynomial is 5.

According to the Fundamental Theorem of Algebra, this polynomial function \( p(x) \) has exactly 5 roots (counting multiplicities).