Find the zeros of h(x). Show your work.

h(x) = -3x^2(5x+8)(x-6)

1 answer

To find the zeros of h(x), we need to find the values of x at which h(x) equals zero.

First, we can set each factor in h(x) equal to zero and solve for x:

-3x^2 = 0
This equation has a zero at x = 0.

5x + 8 = 0
Subtracting 8 from both sides, we get:
5x = -8
Dividing both sides by 5, we get:
x = -8/5

x - 6 = 0
Adding 6 to both sides, we get:
x = 6

So the zeros of h(x) are x = 0, x = -8/5, and x = 6.