Find the zeros of h(x). Show your work.
h(x) = -3x^2(5x+8)(x-6)
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.
To find the zeros of h(x), we need to set h(x) equal to zero and solve for x.
Setting h(x) equal to zero:
-3x^2(5x+8)(x-6) = 0
Now we can solve for x using the zero product property. According to the zero product property, if a product of factors is equal to zero, then at least one of the factors must be equal to zero.
Setting each factor equal to zero:
1) -3x^2 = 0
To solve this, we divide both sides by -3:
x^2 = 0
Taking the square root of both sides, we get:
x = 0
2) 5x + 8 = 0
To solve this, we isolate x by subtracting 8 from both sides:
5x = -8
Then we divide both sides by 5:
x = -8/5
3) x - 6 = 0
To solve this, we simply add 6 to both sides:
x = 6
Therefore, the zeros of h(x) are x = 0, x = -8/5, and x = 6.
Work shown:
-3x^2(5x+8)(x-6) = 0
Setting each factor equal to zero:
-3x^2 = 0
x = 0
5x + 8 = 0
5x = -8
x = -8/5
x - 6 = 0
x = 6
Zeros of h(x):
x = 0, x = -8/5, x = 6