A polynomial equation includes the term 8x5 . According to the Fundamental Theorem of Algebra, which statement must be true?(1 point) Responses The equation has an odd number of real roots. The equation has an odd number of real roots. The equation has at least 5 roots. The equation has at least 5 roots. The equation has more than 5 roots. The equation has more than 5 roots. All the roots of the equation are real.

According to the Fundamental Theorem of Algebra, a polynomial of degree \( n \) has exactly \( n \) roots, counting multiplicities, in the complex number system. In your case, the polynomial has a term \( 8x^5 \), meaning it is of degree 5.

From this, we can conclude that:

- The polynomial has **exactly 5 roots** (which could be real or complex).

Now, let's analyze each of the provided statements:

1. **The equation has an odd number of real roots.** - This statement is not necessarily true; the polynomial could have 5 real roots, 3 real roots and 2 complex roots, 1 real root and 4 complex roots, or 5 complex roots (where complex roots come in conjugate pairs).

2. **The equation has at least 5 roots.** - This statement is true because a degree 5 polynomial has exactly 5 roots, so "at least 5" qualifies.

3. **The equation has more than 5 roots.** - This statement is false since a degree 5 polynomial can only have 5 roots.

4. **All the roots of the equation are real.** - This statement is also not necessarily true; the roots can be a combination of real and complex roots.

Therefore, the correct statement that must be true is:

**The equation has at least 5 roots.**