Final answer:
Yes, it is possible for a third degree polynomial to have no real zeros.
Step-by-step explanation:
Yes, it is possible for a third degree polynomial to have no real zeros.
A polynomial is an expression consisting of variables (such as x), coefficients (such as 3), and exponents (such as 2), combined using operations like addition, subtraction, multiplication, and division.
A third degree polynomial can be written in the form ax^3 + bx^2 + cx + d, where a, b, c, and d are constants. The zeros of a polynomial are the values of x that make the polynomial equal to zero.
For a third degree polynomial to have no real zeros, its graph must not intersect the x-axis at any point. This can happen if the leading coefficient (a) is positive and the polynomial is always either above or below the x-axis without crossing.
For example, the polynomial x^3 + 1 has no real zeros because its graph is always above the x-axis.