Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6 will have.(1 point)%0D%0AResponses%0D%0A%0D%0Athree roots%0D%0Athree roots%0D%0A%0D%0Asix roots%0D%0Asix roots%0D%0A%0D%0Afive roots%0D%0Afive roots%0D%0A%0D%0Aeight 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.

In the given polynomial $y=8x^5-2x^4+6$, the highest power of $x$ is 5, which indicates that the degree of the polynomial is 5.

Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have five roots in total (counting complex roots and multiplicities).

The correct response is five roots.