Final answer:
An odd-degree polynomial would be concluded if a polynomial has only one real non-repeated root, as the Fundamental Theorem of Algebra dictates an odd degree for at least one real root and complex roots in conjugate pairs.
Step-by-step explanation:
If a polynomial has only one real non-repeated root, we can deduce that the order of the polynomial must be odd. This conclusion is based on the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n complex roots, some of which may be repeated. Since we have only one real root and no others are mentioned, it implies that the other roots are complex and come in conjugate pairs.
An odd-degree polynomial will always have at least one real root, and when all other roots are complex, they must be in an even number because complex roots occur in conjugate pairs. Therefore, an odd-degree polynomial with one real non-repeated root implies that the rest of the roots are complex and result in an even count, making the total number of roots (one real and the rest complex) an odd number.