Question

The Fundamental Theorem of Algebra Quick Check
2 of 52 of 5 Items
Question
Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6
will have.(1 point)
Responses

six roots
six roots

eight roots
eight roots

three roots
three roots

five roots
five roots
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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).

The given polynomial is \( y = 8x^5 - 2x^4 + 6 \). The highest degree term is \( 8x^5 \), which indicates that the degree of the polynomial is 5. Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have **five roots** (including complex roots and counting multiplicities).

So, the correct response is:
**five roots**.