How many zeros does a cubic polynomial have?

A cubic polynomial is a polynomial of degree 3, which can be written in the general form:

f(x) = ax^3 + bx^2 + cx + d

where a, b, c, and d are constants, and a ≠ 0 (since it is a cubic polynomial).

To determine how many zeros a cubic polynomial has, we need to consider the following points:

Fundamental Theorem of Algebra: This theorem states that every polynomial equation of degree n (where n is a positive integer) has exactly n roots, counting multiplicities. Therefore, a cubic polynomial (degree 3) must have exactly three roots (zeros), although they may not all be distinct.

Types of Zeros:

A cubic polynomial can have:
Three distinct real roots.
One real root and two complex conjugate roots.
One real root with a multiplicity of three (a triple root).
Thus, a cubic polynomial always has exactly three zeros, though some of them may be repeated or complex.

Conclusion:
A cubic polynomial has exactly three zeros, but they can be real or complex, and they may not all be distinct.