Bot GPT 4-o mini According to the Fundamental Theorem of Algebra, a polynomial equation of degree \( n \) has exactly \( n \) roots in the complex number system, counting multiplicities.
In this case, the term \( 8x^5 \) indicates that the polynomial is of degree 5. Therefore, the statement that must be true is:
The equation has at least 5 roots.
This statement is true because a degree 5 polynomial will have exactly 5 roots when considering complex roots, which includes real and non-real roots. The other statements are not necessarily true. Specifically, the polynomial can have some or all roots that are complex and not just real.
So, the correct response is:
The equation has at least 5 roots.
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