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%0Afive roots%0D%0Afive roots%0D%0A%0D%0Aeight roots%0D%0Aeight roots%0D%0A%0D%0Athree roots%0D%0Athree roots%0D%0A%0D%0Asix roots

Answer 1

The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) will have exactly \( n \) roots (including multiplicities) in the complex number system.

For the polynomial \( y = 8x^5 - 2x^4 + 6 \), the highest degree term is \( 8x^5 \), indicating that this polynomial is of degree 5.

Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have exactly 5 roots (counting multiplicities).

So, the correct response is "five roots."