To determine how many roots the polynomial \( y = 8x^5 - 2x^4 + 6 \) will have, we can use the Fundamental Theorem of Algebra. This theorem states that a polynomial of degree \( n \) will have exactly \( n \) roots in the complex number system (counting multiplicities).
In this case, the highest power of \( x \) in the polynomial is \( 5 \) (from the term \( 8x^5 \)). Therefore, the degree of the polynomial is \( 5 \).
According to the Fundamental Theorem of Algebra, since the degree is \( 5 \), the polynomial \( y = 8x^5 - 2x^4 + 6 \) will have five roots in total.
The correct response is:
five roots