Question

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

Answer 1

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.

Answer 2

the answer for this question is

0.-2,-5