The question is about the general properties of a third-degree polynomial $P(x) = a_3 x^3 + a_2 x^2 + a_1 x + a_0$, and it asks you to determine the number of real roots or zeros that this polynomial might have.

For a third-degree polynomial:

1. It has a maximum of 3 roots (based on its degree).
2. The roots can be real or complex, but due to the nature of polynomials, they must either have one real root and two complex conjugate roots or three real roots (either distinct or with multiplicity).
3. Complex roots appear in conjugate pairs, so a third-degree polynomial cannot have only two real roots.

Given the options:

1. Option (a) "Siempre tendrá más de 3 raíces o ceros reales" (It will always have more than 3 real roots or zeros) – This is incorrect since a polynomial of degree 3 cannot have more than 3 roots.

2. Option (b) "Puede tener 3 raíces reales o menos" (It can have 3 real roots or fewer) – This is correct, as it can have 3 real roots, 2 complex roots and 1 real root, or just one real root, satisfying the possibility of 3 or fewer real roots.

3. Option (c) "Siempre tendrá 3 raíces o ceros reales" (It will always have 3 real roots or zeros) – This is incorrect, as not all third-degree polynomials have 3 real roots; some have only 1 real root with the other two being complex.

4. Option (d) "No tendrá ninguna raíz o cero real" (It will not have any real roots or zeros) – This is incorrect, as a third-degree polynomial will always have at least one real root.

Correct answer: (b) "Puede tener 3 raíces reales o menos."

Would you like more details on why each option is evaluated as such, or do you have any other questions?

Here are some related questions that could expand your understanding:

1. What are the possible real and complex root configurations for polynomials of different degrees?
2. How does the Fundamental Theorem of Algebra determine the number of roots a polynomial can have?
3. What role do complex conjugate roots play in polynomial equations?
4. How can the discriminant of a polynomial help determine the number of real roots?
5. How does the degree of a polynomial influence the behavior of its graph?

Tip: For polynomials of odd degrees, there is always at least one real root due to the Intermediate Value Theorem, as they stretch to $+\infty$ and $-\infty$ at their ends.