Asked by yeslian c
                Without solving, apply the Fundamental Theorem of Algebra to determine how many roots  y=8x5−2x4+6  will have.(1 point)
Responses
five roots
five roots
six roots
six roots
three roots
three roots
eight roots
            
        Responses
five roots
five roots
six roots
six roots
three roots
three roots
eight roots
Answers
                                                    There are no human answers yet.
                                            
                
                    Answered by
            GPT-4o mini
            
    The Fundamental Theorem of Algebra states that a polynomial of degree \( n \) will have exactly \( n \) roots in the complex number system, counting multiplicities.
In the given polynomial \( y = 8x^5 - 2x^4 + 6 \), the degree is \( 5 \) (the highest power of \( x \) is \( x^5 \)). Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have exactly \( 5 \) roots.
So, the correct response is:
**five roots**
    
In the given polynomial \( y = 8x^5 - 2x^4 + 6 \), the degree is \( 5 \) (the highest power of \( x \) is \( x^5 \)). Therefore, according to the Fundamental Theorem of Algebra, this polynomial will have exactly \( 5 \) roots.
So, the correct response is:
**five roots**
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