Q2. - Algebra 2

Question

State the number of turning points of the graph of a fifth-degree polynomial if it has five distinct real zeroes.

Step-by-Step Solution

Answer

The number of turning points of the graph of a fifth-degree polynomial if it has five distinct real zeroes is 4.

Step 1. Given Information.

Given to determine the number of turning points of the graph of a fifth-degree polynomial if it has five distinct real zeroes. 

Step 2. Explanation .

A polynomial has a real zero where the graph crosses the x-axis.

If the polynomial has five distinct real zeroes, it crosses the x-axis five times.

For the graph to cross the x-axis it has to make turn four times i.e. after crossing it once if the graph is going upwards, to cut the x-axis again the graph needs to make a turn downwards.

Step 3. Conclusion .

Hence there are four turning points.