Every polynomial function of degree 3 with real coefficients has exactly three real zeros. True or False?

Polynomial functions are those functions that consist of one or more variables and constants. Depending on the degree of the polynomial, it has a certain number of zeroes.

Answer: It is false that every polynomial function of degree 3 with real coefficients has exactly three real zeros.

Let's understand the solution in detail.

Explanation:

We can have cubic polynomials having less than 3 zeroes.

For example, The polynomial y = x³ + x² + x + 1 has a degree of 3 but has only one real root, that is, x = -1.

The polynomial y = x³ + 11x² + 6x + 1 also has only one zero, that is, x = -0.096.

A cubic polynomial can have a minimum of one zero, as a cubic curve always cuts the x-axis at least once.

Check out more about polynomial functions of degree 3 using the cubic function formula.

Hence, it is false that every polynomial function of degree 3 with real coefficients has exactly three real zeros.