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 three roots three roots eight roots eight roots six roots

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 three roots three roots eight roots eight roots six roots

Answer 1

The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n roots.

In the given polynomial y=8x^5−2x^4+6, the highest power of x is 5, so the degree of the polynomial is 5.

Therefore, the polynomial will have exactly 5 roots.