Question

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

five roots
five roots

six roots
six roots

three roots
three roots

eight roots

Answer 1

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

In the given polynomial \( y = 8x^5 - 2x^4 + 6 \), the degree is \( 5 \) (the highest power of \( x \) is \( x^5 \)). Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have exactly \( 5 \) roots.

So, the correct response is:

**five roots**