The Fundamental Theorem of Algebra Quick Check

Question

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.