Question
Without solving, apply the Fundamental Theorem of Algebra to determine how many roots y=8x5−2x4+6 will have.(1 point) Responses eight roots eight roots six roots six roots five roots five roots three roots
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) has exactly \( n \) roots in the complex number system, counting multiplicities.
In the equation \( y = 8x^5 - 2x^4 + 6 \), the highest degree term is \( 8x^5 \), which indicates that this is a polynomial of degree 5.
Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have **five roots** in total (counting both real and complex roots).
The correct response is **five roots**.
In the equation \( y = 8x^5 - 2x^4 + 6 \), the highest degree term is \( 8x^5 \), which indicates that this is a polynomial of degree 5.
Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have **five roots** in total (counting both real and complex roots).
The correct response is **five roots**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.