Question

Which of the following is a polynomial with a degree of 5, has three distinct zeros, has two zeros with a multiplicity of 2, and has a negative leading coefficient?

Answer 1

Graph 2

Explanation:

The required polynomial is to have the following properties:

• Three distinct zeros

,

• Two zeros with a multiplicity of 2

,

• A negative leading coefficient

,

• A degree of 5.

For the polynomial to satisfy the first two conditions, it must intersect the x-axis at exactly three points and touch the x-axis at a point.

For the polynomial, to satisfy the last two conditions, we use the leading coefficient test.

By one of the conditions of the leading coefficient test: When the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.

The graph that satisfies all these condition is attached below:

The second graph is the correct one.