Chapter 4.5, Problem 48E

To determine

Whether a cubic function can have more than three real zeros.

Answer to Problem 48E

A cubic function cannot have more than three real zeros

Explanation of Solution

Consider a cubic function that is a polynomial with degree 3.

  $f\left(x\right)=a{x}^3+b{x}^2+cx+d$

Here, degree of the function is three.

So, the function can have three factors.

After solving the factors or equating the factors with zero, three solutions can be found.

So, a cubic function cannot have more than three real zeros.