What are the zeros of the function graph the function y=x(x+2)(x+5)

ANSWER

The zeros of

are


EXPLANATION

The given function is


To find the zeros of the above function, we just have to equate the function to zero and solve for x.



This implies that,





To graph the above function, we need to consider the multiplicity.

We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.

We also need to consider the position of the graph on the following intervals,



When


The graph is below the x-axis.


When




The graph is above the x-axis.



when



The graph is below the x-axis.

Finally the interval,


when




The graph is above the x-axis.

We can now use the above information to sketch graph as shown in the diagram above.

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