Question

Tell whether the following statement is always, sometimes or never true. Explain. A polynomial function that has four real roots is a fourth-degree polynomial.

Short answer

The given statement is sometimes true.

Step-by-step solution

Step 1. Given

Given statement is: A polynomial function that has four real roots is a fourth-degree polynomial.

Step 2. To determine

We have to tell and explain whether the following statement is always, sometimes or never true.

Step 3. Calculation

We can draw an even polynomial with four real roots. For example:

This graph is of a 4^th degree polynomial. And it has 4 real roots $-2,-1,1,2$.

We can also draw an odd polynomial with four real roots. For example:

This graph is of a 5^th degree polynomial. And it has 4 real roots $-2,-1,1,2$.

So, the given statement is sometimes true.