Question

the fundamental theorem of algebra quick check
without solving, apply the fundamental theorem of algebra to determine how many roots $y = 8x^5 - 2x^4 + 6$ will have. (1 point)

○ three roots

○ five roots

○ six roots

○ eight roots

Explanation:

Step1: Recall Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) (where \( n \) is a positive integer) has exactly \( n \) roots (counting multiplicities) in the complex number system.

Step2: Determine the degree of the polynomial

For the polynomial \( y = 8x^5 - 2x^4 + 6 \), the highest power of \( x \) is 5. So, the degree \( n \) of the polynomial is 5.

Step3: Apply the theorem to find the number of roots

By the Fundamental Theorem of Algebra, since the degree of the polynomial is 5, the polynomial will have 5 roots (in the complex plane, counting multiplicities).

Answer:

B. five roots