Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6 will have.(1 point)

Question

Responses

three roots
three roots

six roots
six roots

eight roots
eight roots

five roots

Answer 1

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

The polynomial given is \( y = 8x^5 - 2x^4 + 6 \). The degree of this polynomial is determined by the highest power of \( x \), which is \( 5 \) (from the term \( 8x^5 \)).

Therefore, based on the Fundamental Theorem of Algebra, this polynomial will have exactly \( 5 \) roots.

The correct response is:

five roots