Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6

Question

𝑦
=
8
𝑥
5
−
2
𝑥
4
+
6
will have.(1 point)
Responses

five roots
five roots

six roots
six roots

eight roots
eight roots

three 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 case of the polynomial \( y = 8x^5 - 2x^4 + 6 \), the highest degree term is \( 8x^5 \), which indicates that the polynomial is of degree 5.

Therefore, this polynomial will have exactly 5 roots (which may be real or complex).

The correct answer is: five roots.