A polynomial equation includes the term 8x5

Question

8
𝑥
5
. According to the Fundamental Theorem of Algebra, which statement must be true?(1 point)
Responses

The equation has more than 5 roots.
The equation has more than 5 roots.

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

The equation has an odd number of real roots.
The equation has an odd number of real roots.

All the roots of the equation are real.

Answer 1

According to the Fundamental Theorem of Algebra, a polynomial of degree \( n \) has exactly \( n \) roots, counting multiplicities, in the complex number system. The term \( 8x^5 \) indicates that the polynomial is of degree 5.

Therefore, the correct statement is:

The equation has at least 5 roots.

This means that the polynomial must have exactly 5 roots (some of them may be complex or repeated). Hence, it's not guaranteed that all roots are real, nor does it imply an odd number of real roots specifically.