Question

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

Answer 1

The zeros of the function y = x(x+2)(x+5) are x = 0, x = -2, and x = -5.

Step-by-step explanation:

The zeros of a function are the values of x for which the function is equal to zero. To find the zeros of the function y = x(x+2)(x+5), we set y equal to zero and solve for x:

x(x+2)(x+5) = 0

This equation is equal to zero when x = 0, x = -2, or x = -5. Therefore, the zeros of the function are x = 0, x = -2, and x = -5.

Answer 2

ANSWER

The zeros of

`y = x(x + 2)(x + 5)`
are

`x=0,x=-2,x=-5`

EXPLANATION

The given function is

`y = x(x + 2)(x + 5)`

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


`x(x + 2)(x + 5) = 0`

This implies that,


`x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0`


`x = 0 \: \: or \: x = - 2\:or \: x = - 5`

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,


`x < - 5`

When

`x = - 10`

`y = - 10( - 8)( - 5) \: < \: 0`
The graph is below the x-axis.


`- 5 \: < \: x \: < \: - 2`
When

`x = - 3`


`y = - 3(2)( - 1) \: > 0`

The graph is above the x-axis.


`- 2 \: < \: x < \: 0`

when

`x = - 1`


`y = -1(1)(4) \: < \: 0`
The graph is below the x-axis.

Finally the interval,

`x \: > \: 0`

when

`x = 1`


`y = 1(3)(6) \: > \: 0`

The graph is above the x-axis.

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