Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6 will have.(1 point) Responses eight roots eight roots six roots six roots five roots five roots three 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 equation \( y = 8x^5 - 2x^4 + 6 \), the highest degree term is \( 8x^5 \), which indicates that this is a polynomial of degree 5.

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

The correct response is five roots.